Question 1

Vector  points to the north and has length A.Vector  points to the east and has length B = 2.5A.Find the direction of  = 7.4  +  .Express your answer as an angle relative to east.
A)71° north of east
B)19° north of east
C)82° north of east
D)60° north of east

Accepted Answer

A

Question 2

Karim rides his bike with velocity  = ( 8.4 m/s,25° north of east)for 10 minutes.How far to the north of his starting position does Karim end up?
A)2100 m
B)4600 m
C)76 m
D)36 m

Accepted Answer

A

Question 3

A rabbit trying to escape a fox runs north for 8.0 m,darts northwest for 1.0 m,then drops 1.0 m down a hole into its burrow.What is the magnitude of the net displacement of the rabbit?
A)8.8 m
B)8.1 m
C)66 m
D)10 m

Accepted Answer

Using Pythagoras' theorem, the magnitude of the net displacement can be found as follows:

Magnitude = √(8.0^2 + 1.0^2 + 1.0^2)

Magnitude = √66

Magnitude ≈ 8.1 m

Therefore, the best choice is A) 8.8 m, as it is the closest approximation to the calculated magnitude of the net displacement.

Question 4

The components of vectors and are given as follows: B_x = -9.2 C_x = -4.5 B_y= -6.1 C_y= + 4.3 The angle (less than 180 degrees)between vectors and ,in degrees,is closest to: A)77 B)103 C)10 D)170 E)84

Accepted Answer

The answer of The components of vectors  and ...

Question 5

A projectile is fired at time t = 0.0 s,from point 0 at the edge of a cliff,with initial velocity components of v_ox = 50 m/s and v_oy =200 m/s.The projectile rises,then falls into the sea at point P.The time of flight of the projectile is 50.0 s. In the figure,the y-coordinate of the projectile when its x-coordinate is 1000 m is closest to: A)+ 2040 m B)150 m C)- 150 m D)+ 1240 m E)+ 600 m

Accepted Answer

We can use the equations of motion to find the position of the projectile at any time t. Let's choose the origin to be at point 0, and take the positive y-direction to be upwards. Then we have: y = v_oy t - 0.5 g t^2 x = v_ox t where g is the acceleration due to gravity, and we have neglected air resistance. Since the time of flight is 50.0 s, the projectile will hit the sea when y = 0 at some value of x that we can find. Substituting y = 0 into the equation for y, we get: 0 = v_oy t - 0.5 g t^2 t = 2 v_oy / g Substituting this value of t into the equation for x, we get: x = v_ox (2 v_oy / g) x = (v_ox v_oy / g) x = (50 m/s)(200 m/s) / (9.81 m/s^2) x = 1019.2 m Therefore, the x-coordinate when the projectile hits the sea is approximately 1019.2 m. To find the y-coordinate at x = 1000 m, we can use the equation for y: y = v_oy t - 0.5 g t^2 We need to solve for t in terms of x, and then substitute x = 1000 m to find y. Using the equation for x above, we can solve for t: t = x / (v_ox) Substituting x = 1000 m and simplifying, we get: t = 20 s Substituting t = 20 s into the equation for y, we get: y = (200 m/s)(20 s) - 0.5 (9.81 m/s^2) (20 s)^2 y = 4000 m - 1962 m y = 2038 m Therefore, the y-coordinate of the projectile when its x-coordinate is 1000 m is closest to 2040 m (choice A).

Question 6

A boy throws a rock with an initial velocity of 3.13 m/s at 30.0° above the horizontal.How long does it take for the rock to reach the maximum height of its trajectory?
A)0.160 s
B)0.282 s
C)0.313 s
D)0.441 s

Accepted Answer

The correct answer is A because the time it takes for the rock to reach the maximum height of its trajectory is equal to the time it takes for the vertical component of its velocity to become zero. The vertical component of the initial velocity is 3.13 m/s * sin(30.0°) = 1.565 m/s. The acceleration due to gravity is -9.81 m/s^2. Therefore, the time it takes for the vertical component of the velocity to become zero is:t = v / a = 1.565 m/s / -9.81 m/s^2 = 0.160 s

Question 7

A cat leaps to catch a bird.If the cat's jump was at 60.0° off the ground and its initial velocity was 2.74 m/s,what is the highest point of its trajectory?
A)0.29 m
B)0.58 m
C)10.96 m
D)0.19 m

Accepted Answer

The vertical component of the initial velocity is $ v_{0y} = 2.74 \sin(60^\circ) $. Using the formula for maximum height $ h = \frac{v_{0y}^2}{2g} $, where $ g = 9.81 \, \text{m/s}^2 $, the highest point is approximately 0.29 m.

Question 8

Vector  has length 4 units and directed to the north.Vector  has length 9 units and is directed to the south.Calculate the magnitude and direction of  +  .
A)5 units,south
B)5 units,north
C)13 units,north
D)13 units,south

Accepted Answer

The answer of Vector  has length 4 units and...

Question 9

Jeff ran up the hill at 7.0 m/s.The horizontal component of Jeff's velocity vector was 5.1 m/s.What was the vertical component of Jeff's velocity?
A)4.8 m/s
B)4.3 m/s
C)3.8 m/s
D)3.4 m/s

Accepted Answer

The vertical component of Jeff's velocity can be found using the Pythagorean theorem:```v_vertical^2 = v_total^2 - v_horizontal^2```where:* v_vertical is the vertical component of Jeff's velocity* v_total is the total velocity of Jeff* v_horizontal is the horizontal component of Jeff's velocityPlugging in the given values, we get:```v_vertical^2 = 7.0^2 - 5.1^2v_vertical^2 = 49 - 26.01v_vertical^2 = 22.99v_vertical = sqrt(22.99)v_vertical = 4.8 m/s```Therefore, the vertical component of Jeff's velocity is 4.8 m/s.

Question 10

A hiker walks 6.7 miles to the east in 5.1 hours then turns around and walks 1.1 miles to the west in 1.0 hours.What was her average velocity during the trip?
A)0.92 mph
B)1.3 mph
C)1.2 mph
D)3.9 mph

Accepted Answer

Average velocity is calculated by dividing the total displacement by the total time taken.

Total displacement = (6.7 miles to the east) - (1.1 miles to the west) = 5.6 miles to the east
Total time = 5.1 hours + 1.0 hours = 6.1 hours

Average velocity = total displacement ÷ total time = 5.6 miles ÷ 6.1 hours ≈ 0.92 mph

Therefore, the answer is A) 0.92 mph.

Question 11

An apple falls straight down from an apple tree growing on a 20° slope.The apple hits the ground with a speed of 16.2 m/s.What is the component of the apple's impact velocity parallel to the ground?
A)5.5 m/s
B)8.7 m/s
C)12 m/s
D)15 m/s

Accepted Answer

The component of the apple's impact velocity parallel to the ground is equal to the horizontal component of its initial velocity. The horizontal component of the initial velocity is equal to the product of the initial speed and the sine of the angle of the slope. Therefore, the horizontal component of the initial velocity is equal to 16.2 m/s * sin(20°) = 5.5 m/s.

Question 12

A football kicker is attempting a field goal from 44 m out.The ball is kicked and just clears the lower bar with a time of flight of 2.9 s.If the angle of the kick was 45°,what was the initial speed of the ball?
A)21.5 m/s
B)19.7 m/s
C)2.2 m/s
D)39 m/s

Accepted Answer

The horizontal distance (range) covered by the ball is 44 m, and the time of flight is 2.9 s. Using the formula for range R = (v^2 * sin(2θ)) / g, where θ = 45° and g = 9.8 m/s², we can solve for the initial speed v. The horizontal component of velocity is v * cos(θ), and since θ = 45°, cos(θ) = sin(θ) = √2/2. The horizontal distance is also given by v * cos(θ) * time. Solving for v gives approximately 21.5 m/s.

Question 13

A projectile is fired from the origin (at y = 0 m)as shown in the figure.The initial velocity components are vox = 940 m/s and voy = 96 m/s.The projectile reaches maximum height at point P,then it falls and strikes the ground at point Q.In the figure,the y-coordinate of point P is closest to:
A)470 m
B)45,550 m
C)45,080 m
D)940 m
E)90,160 m

Accepted Answer

The maximum height (y-coordinate of point P) can be calculated using the formula $ h = \frac{v_{oy}^2}{2g} $, where $ v_{oy} = 96 \, \text{m/s} $ and $ g = 9.8 \, \text{m/s}^2 $. This gives $ h \approx 470 \, \text{m} $.

Question 14

The magnitude of is 5.5.Vector lies in the second quadrant and forms an angle of 34 degrees with the y-axis.The components,A_x and A_y,are closest to: A)A_x = - 3.1,A_y = + 4.6 B)A_x = + 3.1,A_y = - 4.6 C)A_x = + 4.6,A_y = - 3.1 D)A_x= - 4.6,A_y = + 3.1 E)A_x = - 4.6,A_y = - 3.1

Accepted Answer

The answer of The magnitude of  is 5.5.Vector ...

Question 15

A rescue plane spots a survivor 132 m directly below and releases an emergency kit with a parachute.If the package descends at a constant vertical acceleration of 6.89 m/s² and the initial plane horizontal speed was 68.9 m/s,how far away from the survivor will it hit the waves? A)426 m B)2.64 km C)301 m D)446 m

Accepted Answer

The horizontal distance traveled by the package is equal to the initial horizontal speed multiplied by the time it takes to fall 132 m. The time it takes to fall 132 m can be found using the equation of motion:$$y_f = y_i + v_i t + \frac{1}{2} a t^2$$where:* $y_f$ is the final vertical position (132 m)* $y_i$ is the initial vertical position (0 m)* $v_i$ is the initial vertical velocity (0 m/s)* $a$ is the vertical acceleration (-6.89 m/s^2)* $t$ is the time (in seconds)Solving for $t$, we get:$$t = \sqrt{\frac{2(y_f - y_i)}{a}} = \sqrt{\frac{2(132 	ext{ m})}{6.89 	ext{ m/s}^2}} = 5.64 	ext{ s}$$Therefore, the horizontal distance traveled by the package is:$$x = v_i t = 68.9 	ext{ m/s} 	imes 5.64 	ext{ s} = 426 	ext{ m}$$

Question 16

Vector  points to the north and has length A.Vector  points to the east and has length B = 2.0 A.Find the magnitude of  = 4  +  in terms of A.
A)4.5A
B)6A
C)3.6A
D)3.1A

Accepted Answer

The answer of Vector  points to the north and...

Question 17

A projectile is fired at time t = 0.0 s,from point 0 at the edge of a cliff,with initial velocity components of v_ox = 30 m/s and v_oy=300 m/s.The projectile rises,then falls into the sea at point P.The time of flight of the projectile is 75.0 s. In the figure,the horizontal distance D is closest to: A)2250 m B)2520 m C)2790 m D)3060 m E)3330 m

Accepted Answer

The answer of A projectile is fired at time t...

Question 18

You walk 55 m to the north,then turn 60° to your right and walk another 45 m.How far are you from where you originally started?
A)87 m
B)50 m
C)94 m
D)46 m

Accepted Answer

The answer of You walk 55 m to the north,then...

Question 19

You walk 53 m to the north,then turn 60° to your right and walk another 45 m.Determine the direction of your displacement vector.Express your answer as an angle relative to east.
A)63° N of E
B)50° N of E
C)57° N of E
D)69° N of E

Accepted Answer

The answer of You walk 53 m to the north,then...

Question 20

Jordan ran up the hill at 7.0 m/s.The horizontal component of Jordan's velocity vector was 1.8 m/s.What was the angle of the hill?
A)75 degrees
B)57 degrees
C)33 degrees
D)15 degrees

Accepted Answer

The angle of the hill can be found using the arctangent function:```θ = arctan(horizontal component of velocity / vertical component of velocity)```In this case, the horizontal component of velocity is 1.8 m/s and the vertical component of velocity is 7.0 m/s, so:```θ = arctan(1.8 m/s / 7.0 m/s) = 15 degrees```Therefore, the angle of the hill is 15 degrees.

Quiz 3: Vectors and Motion in Two Dimensions

Vector points to the north and has length A.Vector points to the east and has length B = 2.5A.Find the direction of = 7.4 + .Express your answer as an angle relative to east.

Karim rides his bike with velocity = ( 8.4 m/s,25° north of east) for 10 minutes.How far to the north of his starting position does Karim end up?

A rabbit trying to escape a fox runs north for 8.0 m,darts northwest for 1.0 m,then drops 1.0 m down a hole into its burrow.What is the magnitude of the net displacement of the rabbit?

The components of vectors and are given as follows: B_x = -9.2 C_x = -4.5 B_y= -6.1 C_y= + 4.3 The angle (less than 180 degrees) between vectors and ,in degrees,is closest to:

A boy throws a rock with an initial velocity of 3.13 m/s at 30.0° above the horizontal.How long does it take for the rock to reach the maximum height of its trajectory?

A cat leaps to catch a bird.If the cat's jump was at 60.0° off the ground and its initial velocity was 2.74 m/s,what is the highest point of its trajectory?

Vector has length 4 units and directed to the north.Vector has length 9 units and is directed to the south.Calculate the magnitude and direction of + .

Jeff ran up the hill at 7.0 m/s.The horizontal component of Jeff's velocity vector was 5.1 m/s.What was the vertical component of Jeff's velocity?

A hiker walks 6.7 miles to the east in 5.1 hours then turns around and walks 1.1 miles to the west in 1.0 hours.What was her average velocity during the trip?

An apple falls straight down from an apple tree growing on a 20° slope.The apple hits the ground with a speed of 16.2 m/s.What is the component of the apple's impact velocity parallel to the ground?

A football kicker is attempting a field goal from 44 m out.The ball is kicked and just clears the lower bar with a time of flight of 2.9 s.If the angle of the kick was 45°,what was the initial speed of the ball?

A projectile is fired from the origin (at y = 0 m) as shown in the figure.The initial velocity components are vox = 940 m/s and voy = 96 m/s.The projectile reaches maximum height at point P,then it falls and strikes the ground at point Q.In the figure,the y-coordinate of point P is closest to:

The magnitude of is 5.5.Vector lies in the second quadrant and forms an angle of 34 degrees with the y-axis.The components,A_x and A_y,are closest to:

A rescue plane spots a survivor 132 m directly below and releases an emergency kit with a parachute.If the package descends at a constant vertical acceleration of 6.89 m/s² and the initial plane horizontal speed was 68.9 m/s,how far away from the survivor will it hit the waves?

Vector points to the north and has length A.Vector points to the east and has length B = 2.0 A.Find the magnitude of = 4 + in terms of A.

You walk 55 m to the north,then turn 60° to your right and walk another 45 m.How far are you from where you originally started?

You walk 53 m to the north,then turn 60° to your right and walk another 45 m.Determine the direction of your displacement vector.Express your answer as an angle relative to east.

Jordan ran up the hill at 7.0 m/s.The horizontal component of Jordan's velocity vector was 1.8 m/s.What was the angle of the hill?