Question 1

A displacement vector is 34.0 m in length and is directed 60.0° east of north. What are the components of this vector?

A) Choice 1
B) Choice 2
C) Choice 3
D) Choice 4
E) Choice 5

Accepted Answer

The answer of A displacement vector is 34.0 m in...

Question 2

A player throws a football 50.0 m at 61.0° north of west. The westward component of the displacement of the football thrown is given by
A) 64.7 m.
B) 55.0 m.
C) 0 m.
D) 74.0 m.
E) 24.2 m.

Accepted Answer

The westward component of the displacement can be found using the cosine function, as it represents the adjacent side in the right triangle formed by the displacement vector. Thus, $westward\ component = 50.0\ m \times \cos(61.0°) \approx 24.2\ m$.

Question 3

If I walk 8.0 meters in a straight line and then walk 5.0 meters in another straight line, the total displacement cannot have a magnitude of
A) 3. m.
B) 2. m.
C) 13. m.
D) 5. m.
E) 8. m.

Accepted Answer

The total displacement is the straight-line distance between the starting and ending points. The minimum displacement occurs when the two walks are in opposite directions, resulting in a displacement of 3 meters (8 - 5), and the maximum displacement occurs when the walks are in the same direction, resulting in a displacement of 13 meters (8 + 5). A displacement of 2 meters is not possible.

Question 4

A boy jumps at a speed of 20.0 m/s at an angle of 25.0° above the horizontal. What is the horizontal component of the boy's velocity?
A) 12.6 m/s
B) 8.5 m/s
C) 18.1 m/s
D) 15.6 m/s
E) 20.0 m/s

Accepted Answer

The horizontal component of the velocity can be found using the formula $v_x = v \cos(\theta)$, where $v = 20.0 \, \text{m/s}$ is the initial velocity and $\theta = 25.0^\circ$ is the angle. Calculating this gives $v_x = 20.0 \cos(25.0^\circ) \approx 18.1 \, \text{m/s}$.

Question 5

A butterfly moves with a speed of v = 12.0 m/s. The x-component of its velocity is 8.00 m/s. The angle between the direction of its motion and the x-axis must be
A) 30.0°
B) 41.8°
C) 53.0°
D) 60.0°
E) 48.2°

Accepted Answer

The answer of A butterfly moves with a speed of...

Question 6

A train traveling at 50. km/h approaches another train moving toward the first at 90. km/h. If they are 35. km apart (on a straight track) how long does it take before they meet?
A) 45. min
B) 25. min
C) 55. min
D) 30. min
E) 15. min

Accepted Answer

The answer of A train traveling at 50. km/h approaches...

Question 7

An electron, initially moving at 2.0 × 10⁴ m/s along the +x-axis, experiences a constant acceleration of 1010 m/s² in the +y direction. How far from its starting point is the electron after 4.0 × 10^-6 seconds? A) 8.0 m B) 11.3 m C) 11.3 cm D) 8.0 cm E) 9.8 m

Accepted Answer

The electron moves in the x-direction with constant velocity and in the y-direction with constant acceleration. The distance in the x-direction is (2.0 × 10^4 m/s) × (4.0 × 10^-6 s) = 0.08 m. The distance in the y-direction is (1/2) × (1010 m/s²) × (4.0 × 10^-6 s)² = 8.08 × 10^-6 m. The total distance is √((0.08 m)² + (8.08 × 10^-6 m)²) ≈ 0.113 m or 11.3 cm.

Question 8

A vector has components A_x = 12 m and A_y = 5.0 m. What is the magnitude of vector ? A) 13 m B) 17 m C) 21 m D) 60 m E) 7.0 m

Accepted Answer

The answer of A vector has components A_x =...

Question 9

A vector has components A_x = 12.0 m and A_y = 5.00 m. What is the angle that vector makes with the x-axis? A) 32.6° B) 12.6° C) 22.6° D) 6.6° E) 42.8°

Accepted Answer

The answer of A vector has components A_x =...

Question 10

Three vectors, expressed in Cartesian coordinates, are
 
The magnitude of the resultant vector is
A) 5.5
B) 13.0
C) 11.1
D) 7.0
E) 2.0

Accepted Answer

The answer of Three vectors, expressed in Cartesian coordinates, are
...

Question 11

If vector = -3.0 ^x - 4.0 ^y , and vector = +3.0^x -8.0 ^y, then the magnitude of = - is A) 144 B) 16 C) 7.2 D) 3.0 E) 13.4

Accepted Answer

The answer of If vector = -3.0 ^x -...

Question 12

A ball thrown horizontally from a point 24 m above the ground strikes the ground after traveling horizontally a distance of 18 m. With what speed was it thrown? (in this problem use g = 10 m/s²) A) 7.40 m/s B) 8.13 m/s C) 8.96 m/s D) g E) 6.10 m/s

Accepted Answer

The answer of A ball thrown horizontally from a point...

Question 13

Janice throws a stone horizontally from the roof edge of a 50. meter high dormitory. It hits the ground at a point 60. m from the building. What was the initial velocity?
A)  g m/s
B) 25. m/s
C) 5.5 m/s
D) 22. m/s
E) 19. m/s

Accepted Answer

The answer of Janice throws a stone horizontally from the...

Question 14

A plane flying horizontally at a speed of 50.0 m/s and at an elevation of 160. m drops a package of supplies. Two seconds later it drops a second package. How far apart will the two packages land on the ground?
A) 162. m
B) 177. m
C) 67.7 m
D) 100. m
E) 283. m

Accepted Answer

The horizontal distance between the two packages is determined by the horizontal speed of the plane and the time interval between the drops. The plane travels 50.0 m/s * 2 s = 100 m in the 2 seconds between the drops.

Question 15

A girl throws a rock horizontally, with a velocity of 10 m/s, from a bridge. It falls 20 m to the water below. How far does the rock travel horizontally before striking the water? (use g = 10 m/s²) A) 14 m B) 16 m C) 24 m D) 20 m E) 12 m

Accepted Answer

The time it takes for the rock to fall 20 m can be calculated using the formula for free fall: $ t = \sqrt{\frac{2h}{g}} = \sqrt{\frac{2 \times 20}{10}} = 2 $ seconds. The horizontal distance is then $ \text{velocity} \times \text{time} = 10 \, \text{m/s} \times 2 \, \text{s} = 20 \, \text{m} $.

Question 16

A basketball is thrown with a velocity of 20. m/s at an angle of 60.° above the horizontal. What is the horizontal component of its instantaneous velocity at the exact top of its trajectory? (Neglect air friction.)
A) 10. m/s
B) 20. m/s
C) zero
D) 17.3 m/s
E) 20. tan(60°) m/s

Accepted Answer

At the top of its trajectory, the vertical component of the velocity is zero, but the horizontal component remains constant. The horizontal component is given by 20 m/s * cos(60°) = 10 m/s.

Question 17

A fighter plane moving 200 m/s fires a projectile with speed 50 m/s in a forward direction. The projectile makes an angle of 30° with the direction of the plane's motion. What is the speed of the projectile with respect to a stationary observer on the ground?
A) 243 m/s
B) 293 m/s
C) 281 m/s
D) 250 m/s
E) 268 m/s

Accepted Answer

The speed of the projectile with respect to the stationary observer on the ground is the vector sum of the speed of the projectile with respect to the fighter plane and the speed of the fighter plane with respect to the ground. The speed of the projectile with respect to the fighter plane is 50 m/s at an angle of 30° with the direction of the plane's motion. The speed of the fighter plane with respect to the ground is 200 m/s. The vector sum of these two velocities is 243 m/s at an angle of 15° with the direction of the plane's motion.

Question 18

John can hit a golf ball 310. m on Earth. On the moon's surface, g = ^g earth, so how far could he hit the same ball if he could only achieve half the initial speed at the same angle as that achieved on Earth? A) 396. m B) 155. m C) 465. m D) 1860. m E) 78. m

Accepted Answer

The answer of John can hit a golf ball 310....

Question 19

A motorcycle stunt rider wants to jump a 179. m wide canyon. He arranges a ramp on one side so he will be launched pointed 30.° above the horizontal. What minimum speed will be needed to just reach the other side?
A) 30. m/s
B) 35. m/s
C) 45. m/s
D) 40. m/s
E) 25. m/s

Accepted Answer

To find the minimum speed, use the projectile motion formula: range = (v^2 * sin(2θ)) / g. Solving for v with range = 179 m, θ = 30°, and g = 9.8 m/s² gives approximately 45 m/s.

Question 20

Johnny throws a shotput at an angle of 45.° and it travels a horizontal distance of 30. meters. If he releases the shotput at the same speed but changes the angle to 55.°, what will be the new range (distance)?
A) 37. m
B) 25. m
C) 28. m
D) 41. m
E) 32. m

Accepted Answer

The range of a projectile is maximized at 45°. Increasing the angle to 55° will decrease the range. Using the range formula and adjusting for the angle, the new range is approximately 28 meters.

Quiz 3: Motion in Two Dimensions

A displacement vector is 34.0 m in length and is directed 60.0° east of north. What are the components of this vector?

A player throws a football 50.0 m at 61.0° north of west. The westward component of the displacement of the football thrown is given by

If I walk 8.0 meters in a straight line and then walk 5.0 meters in another straight line, the total displacement cannot have a magnitude of

A boy jumps at a speed of 20.0 m/s at an angle of 25.0° above the horizontal. What is the horizontal component of the boy's velocity?

A butterfly moves with a speed of v = 12.0 m/s. The x-component of its velocity is 8.00 m/s. The angle between the direction of its motion and the x-axis must be

A train traveling at 50. km/h approaches another train moving toward the first at 90. km/h. If they are 35. km apart (on a straight track) how long does it take before they meet?

An electron, initially moving at 2.0 × 10⁴ m/s along the +x-axis, experiences a constant acceleration of 1010 m/s² in the +y direction. How far from its starting point is the electron after 4.0 × 10^-6 seconds?

A vector has components A_x = 12 m and A_y = 5.0 m. What is the magnitude of vector 11eea3cd_97cf_6a5c_97f4_87e191913ebf_TB9720_11?

A vector has components A_x = 12.0 m and A_y = 5.00 m. What is the angle that vector 11eea3cd_97cf_6a5c_97f4_87e191913ebf_TB9720_11 makes with the x-axis?

Three vectors, expressed in Cartesian coordinates, are The magnitude of the resultant vector is

If vector = -3.0 ^x - 4.0 ^y , and vector = +3.0^x -8.0 ^y, then the magnitude of vector= - 11eea3ce_f582_45ef_97f4_e39aa9df0df9_TB9720_11 is

A ball thrown horizontally from a point 24 m above the ground strikes the ground after traveling horizontally a distance of 18 m. With what speed was it thrown? (in this problem use g = 10 m/s²)

Janice throws a stone horizontally from the roof edge of a 50. meter high dormitory. It hits the ground at a point 60. m from the building. What was the initial velocity?

A plane flying horizontally at a speed of 50.0 m/s and at an elevation of 160. m drops a package of supplies. Two seconds later it drops a second package. How far apart will the two packages land on the ground?

A girl throws a rock horizontally, with a velocity of 10 m/s, from a bridge. It falls 20 m to the water below. How far does the rock travel horizontally before striking the water? (use g = 10 m/s²)

A basketball is thrown with a velocity of 20. m/s at an angle of 60.° above the horizontal. What is the horizontal component of its instantaneous velocity at the exact top of its trajectory? (Neglect air friction.)

A fighter plane moving 200 m/s fires a projectile with speed 50 m/s in a forward direction. The projectile makes an angle of 30° with the direction of the plane's motion. What is the speed of the projectile with respect to a stationary observer on the ground?

John can hit a golf ball 310. m on Earth. On the moon's surface, g = ^g earth, so how far could he hit the same ball if he could only achieve half the initial speed at the same angle as that achieved on Earth?

A motorcycle stunt rider wants to jump a 179. m wide canyon. He arranges a ramp on one side so he will be launched pointed 30.° above the horizontal. What minimum speed will be needed to just reach the other side?

Johnny throws a shotput at an angle of 45.° and it travels a horizontal distance of 30. meters. If he releases the shotput at the same speed but changes the angle to 55.°, what will be the new range (distance) ?

Quiz 3: Motion in Two Dimensions

A displacement vector is 34.0 m in length and is directed 60.0° east of north. What are the components of this vector?

A player throws a football 50.0 m at 61.0° north of west. The westward component of the displacement of the football thrown is given by

If I walk 8.0 meters in a straight line and then walk 5.0 meters in another straight line, the total displacement cannot have a magnitude of

A boy jumps at a speed of 20.0 m/s at an angle of 25.0° above the horizontal. What is the horizontal component of the boy's velocity?

A butterfly moves with a speed of v = 12.0 m/s. The x-component of its velocity is 8.00 m/s. The angle between the direction of its motion and the x-axis must be

A train traveling at 50. km/h approaches another train moving toward the first at 90. km/h. If they are 35. km apart (on a straight track) how long does it take before they meet?

An electron, initially moving at 2.0 × 104 m/s along the +x-axis, experiences a constant acceleration of 1010 m/s2 in the +y direction. How far from its starting point is the electron after 4.0 × 10-6 seconds?

A vector has components Ax = 12 m and Ay = 5.0 m. What is the magnitude of vector 11eea3cd_97cf_6a5c_97f4_87e191913ebf_TB9720_11?

A vector has components Ax = 12.0 m and Ay = 5.00 m. What is the angle that vector 11eea3cd_97cf_6a5c_97f4_87e191913ebf_TB9720_11 makes with the x-axis?

Three vectors, expressed in Cartesian coordinates, are The magnitude of the resultant vector is

If vector = -3.0 x - 4.0 y , and vector = +3.0 x -8.0 y , then the magnitude of vector= - 11eea3ce_f582_45ef_97f4_e39aa9df0df9_TB9720_11 is

A ball thrown horizontally from a point 24 m above the ground strikes the ground after traveling horizontally a distance of 18 m. With what speed was it thrown? (in this problem use g = 10 m/s2)

Janice throws a stone horizontally from the roof edge of a 50. meter high dormitory. It hits the ground at a point 60. m from the building. What was the initial velocity?

A plane flying horizontally at a speed of 50.0 m/s and at an elevation of 160. m drops a package of supplies. Two seconds later it drops a second package. How far apart will the two packages land on the ground?

A girl throws a rock horizontally, with a velocity of 10 m/s, from a bridge. It falls 20 m to the water below. How far does the rock travel horizontally before striking the water? (use g = 10 m/s2)

A basketball is thrown with a velocity of 20. m/s at an angle of 60.° above the horizontal. What is the horizontal component of its instantaneous velocity at the exact top of its trajectory? (Neglect air friction.)

A fighter plane moving 200 m/s fires a projectile with speed 50 m/s in a forward direction. The projectile makes an angle of 30° with the direction of the plane's motion. What is the speed of the projectile with respect to a stationary observer on the ground?

John can hit a golf ball 310. m on Earth. On the moon's surface, g = g earth, so how far could he hit the same ball if he could only achieve half the initial speed at the same angle as that achieved on Earth?

A motorcycle stunt rider wants to jump a 179. m wide canyon. He arranges a ramp on one side so he will be launched pointed 30.° above the horizontal. What minimum speed will be needed to just reach the other side?

Johnny throws a shotput at an angle of 45.° and it travels a horizontal distance of 30. meters. If he releases the shotput at the same speed but changes the angle to 55.°, what will be the new range (distance) ?

An electron, initially moving at 2.0 × 10⁴ m/s along the +x-axis, experiences a constant acceleration of 1010 m/s² in the +y direction. How far from its starting point is the electron after 4.0 × 10^-6 seconds?

A vector has components A_x = 12 m and A_y = 5.0 m. What is the magnitude of vector 11eea3cd_97cf_6a5c_97f4_87e191913ebf_TB9720_11?

A vector has components A_x = 12.0 m and A_y = 5.00 m. What is the angle that vector 11eea3cd_97cf_6a5c_97f4_87e191913ebf_TB9720_11 makes with the x-axis?

If vector = -3.0 ^x - 4.0 ^y , and vector = +3.0^x -8.0 ^y, then the magnitude of vector= - 11eea3ce_f582_45ef_97f4_e39aa9df0df9_TB9720_11 is

A ball thrown horizontally from a point 24 m above the ground strikes the ground after traveling horizontally a distance of 18 m. With what speed was it thrown? (in this problem use g = 10 m/s²)

A girl throws a rock horizontally, with a velocity of 10 m/s, from a bridge. It falls 20 m to the water below. How far does the rock travel horizontally before striking the water? (use g = 10 m/s²)

John can hit a golf ball 310. m on Earth. On the moon's surface, g = ^g earth, so how far could he hit the same ball if he could only achieve half the initial speed at the same angle as that achieved on Earth?