Question 1

A stone thrown from the top of a tall building follows a path that is:
A)circular
B)made of two straight line segments
C)hyperbolic
D)parabolic
E)a straight line

Accepted Answer

When an object is thrown from a height, ignoring air resistance, it follows a parabolic path due to gravity pulling it downwards.

Question 2

A bullet shot horizontally from a gun:
A)strikes the ground much later than one dropped vertically from the same point at the same instant
B)never strikes the ground
C)strikes the ground at approximately the same time as one dropped vertically from the same point at the same instant
D)travels in a straight line
E)strikes the ground much sooner than one dropped from the same point at the same instant

Accepted Answer

Both bullets, one dropped vertically and one shot horizontally, will hit the ground at approximately the same time. This is because both bullets experience the same acceleration due to gravity, regardless of their initial horizontal velocity. Therefore, their vertical motion (falling towards the ground) is the same.

Question 3

An airplane is flying north at 500 km/h.It makes a gradual 180$\degree$ turn at constant speed, changing its direction of travel from north through east to south.The process takes 40 s.The average acceleration of the plane for this turn is:
A)12.5 km/h.s, north
B)12.5 km/h.s, east
C)12.5 km/h.s, south
D)25 km/h.s, north
E)25 km/h.s, south

Accepted Answer

The average acceleration can be calculated using the change in velocity over time. The plane changes its velocity direction from north to south, maintaining the same speed. The magnitude of the velocity change is twice the speed (500 km/h north to 500 km/h south), which is 1000 km/h. Over 40 seconds, the average acceleration is $ \frac{1000 \, \text{km/h}}{40 \, \text{s}} = 25 \, \text{km/h} \cdot \text{s}^{-1} $, directed south because the change in velocity is towards the south.

Question 4

An airplane makes a gradual 90$\degree$ turn while flying at a constant speed of 200 m/s.The process takes 20.0 seconds to complete.For this turn the magnitude of the average acceleration of the plane is: A)0 m/s² B)40 m/s² C)20 m/s² D)14 m/s² E)10 m/s²

Accepted Answer

The average acceleration can be found using the formula:
average acceleration = change in velocity/change in time

Since the speed of the plane is constant, the change in velocity is equal to zero. Therefore, the average acceleration is also equal to zero.

However, the question asks for the magnitude of the average acceleration, which is the absolute value of the average acceleration. Therefore, the answer is still zero or choice D.

Question 5

The airplane shown is in level flight at an altitude of 0.50 km and a speed of 150 km/h.At what distance d should it release a heavy bomb to hit the target X? Take g = 10 m/s². A)150 m B)295 m C)417 m D)1500 m E)15,000 m

Accepted Answer

The answer of The airplane shown is in level flight...

Question 6

A boy on the edge of a vertical cliff 20 m high throws a stone horizontally outwards with a speed of 20 m/s.It strikes the ground at what horizontal distance from the foot of the cliff? Use g = 10 m/s² A)10 m B)40 m C)50 m D)50.0 m E)none of these

Accepted Answer

Horizontal distance = (u * t) = (20 * 2) = 40 m

Question 7

A stone is tied to a string and whirled at constant speed in a horizontal circle.The speed is then doubled without changing the length of the string.Afterward the magnitude of the acceleration of the stone is:
A)the same
B)twice as great
C)four times as great
D)half as great
E)one-fourth as great

Accepted Answer

The acceleration of an object moving in a circle is given by the equation a = v^2/r, where v is the speed of the object and r is the radius of the circle. When the speed of the stone is doubled without changing the length of the string, the radius of the circle remains the same, but the speed v increases. Plugging in v' = 2v into the equation, we get a' = (2v)^2/r = 4(v^2/r). Therefore, the magnitude of the acceleration of the stone is four times as great as it was before.

Question 8

A cannon fires a projectile as shown.The dashed line shows the trajectory in the absence of gravity; points MNOP correspond to the position of the projectile at one second intervals.If g = 10 m/s², the lengths X,Y,Z are: A)5 m, 10 m, 15 m B)5 m, 20 m, 45 m C)10 m, 40 m, 90 m D)10 m, 20 m, 30 m E)0.2 m, 0.8 m, 1.8 m

Accepted Answer

The answer of A cannon fires a projectile as shown.The...

Question 9

Two objects are traveling around different circular orbits with constant speed.They both have the same acceleration but object A is traveling twice as fast as object B.The orbit radius for object A is _______ the orbit radius for object B.
A)one-fourth
B)one-half
C)the same as
D)twice
E)four times

Accepted Answer

The centripetal acceleration formula is $a = \frac{v^2}{r}$, where $a$ is the acceleration, $v$ is the velocity, and $r$ is the radius of the circular path. Given that both objects have the same acceleration but object A is traveling twice as fast as object B ($v_A = 2v_B$), we can set their accelerations equal to each other: $\frac{(2v_B)^2}{r_A} = \frac{v_B^2}{r_B}$. Simplifying gives $\frac{4v_B^2}{r_A} = \frac{v_B^2}{r_B}$, which further simplifies to $r_A = 4r_B$. Thus, the orbit radius for object A is four times the orbit radius for object B.

Question 10

A toy racing car moves with constant speed around the circle shown below.When it is at point A its coordinates are x = 0, y = 3m and its velocity is (6 m/s).When it is at point B its velocity and acceleration are: A)−(6 m/s)and (12 m/s²), respectively B)(6 m/s)and −(12 m/s²), respectively C)(6 m/s)and (12 m/s²), respectively D)(6 m/s)and (12 m/s³), respectively E)(6 m/s)and 0 m/s², respectively

Accepted Answer

The answer of A toy racing car moves with constant...

Question 11

An object is moving on a circular path of radius $\pi$ meters at a constant speed of 4.0 m/s.The time required for one revolution is: A)"2/ $\pi$² s" B)" $\pi$²/2 s" C)" $\pi$/2 s" D)" $\pi$²/4 s" E)"2/ $\pi$ s"

Accepted Answer

The time required for one revolution (period) is given by the formula T=2πr/v, where r is the radius of the circle and v is the constant speed. Plugging in the values, we get T=2π(F1F1F1S1πF1F1F10)/(4.0) = F1F1F1S1πF1F1F10/2 seconds. Therefore, the answer is B.

Question 12

A particle moves at constant speed in a circular path.The instantaneous velocity and instantaneous acceleration vectors are:
A)both tangent to the circular path
B)both perpendicular to the circular path
C)perpendicular to each other
D)opposite to each other
E)none of the above

Accepted Answer

The instantaneous velocity vector of a particle moving in a circular path is always tangent to the circle at the particle's position, while the instantaneous acceleration vector (centripetal acceleration) is always directed towards the center of the circle, making them perpendicular to each other.

Question 13

A stone is thrown outward from the top of a 59.4-m high cliff with an upward velocity component of 19.5 m/s.How long is the stone in the air? Assume that it lands on the ground below the cliff, and that the ground below the cliff is flat.
A)4.00 s
B)5.00 s
C)6.00 s
D)7.00 s
E)8.00 s

Accepted Answer

Using the kinematic equation, $y = v_{0y}t + \frac{1}{2}at^2$, where $y$ is the vertical displacement, $v_{0y}$ is the initial vertical velocity, $a$ is the acceleration due to gravity, and $t$ is the time elapsed, we can solve for $t$ when the stone hits the ground.
$$y = v_{0y}t + \frac{1}{2}at^2$$
$$0 = 19.5t - \frac{1}{2}gt^2 - 59.4$$
where $g$ is the acceleration due to gravity, $g = 9.81 	ext{ m/s}^2$
Using the quadratic formula, we get
$$t = \frac{-19.5 \pm \sqrt{(19.5)^2 - 4(-\frac{1}{2}g)(-59.4)}}{-g}$$
$$t = \frac{-19.5 \pm \sqrt{1511}}{-4.905}$$
Since we want the positive solution (the stone can't be in the air for a negative time), we take
$$t = \frac{-19.5 + \sqrt{1511}}{-4.905} \approx 6.00 	ext{ s}$$
Therefore, the best choice for the answer is (C) 6.00 s.

Question 14

Two projectiles are in flight at the same time.The acceleration of one relative to the other: A)is always 9.8 m/s² B)can be as large as 19.6 m/s² C)can be horizontal D)is zero E)none of these

Accepted Answer

The acceleration of each projectile is solely dependent on the forces acting upon it, which are independent of each other. Therefore, the acceleration of one projectile with respect to the other is zero.

Question 15

A dart is thrown horizontally toward X at 20 m/s as shown.It hits Y 0.1 s later.The distance XY is: 
A)2 m
B)1 m
C)0.5 m
D)0.1 m
E)0.05 m

Accepted Answer

The answer of A dart is thrown horizontally toward X...

Question 16

A ball is thrown horizontally from the top of a 20-m high hill.It strikes the ground at an angle of 45$\degree$.With what speed was it thrown? Use g = 10 m/s². A)14 m/s B)20 m/s C)28 m/s D)32 m/s E)40 m/s

Accepted Answer

The answer of A ball is thrown horizontally from the...

Question 17

A large cannon is fired from ground level over level ground at an angle of 30$\degree$ above the horizontal.The muzzle speed is 980 m/s.Neglecting air resistance, the projectile will travel what horizontal distance before striking the ground?
A)4.3 km
B)8.5 km
C)43 km
D)85 km
E)170 km

Accepted Answer

The answer of A large cannon is fired from ground...

Question 18

An object is shot from the back of a railroad flatcar moving at 40 km/h on a straight horizontal road.The launcher is aimed upward, perpendicular to the bed of the flatcar.The object falls:
A)in front of the flatcar
B)behind the flatcar
C)on the flatcar
D)either behind or in front of the flatcar, depending on the initial speed of the object
E)to the side of the flatcar

Accepted Answer

The object maintains the horizontal velocity of the flatcar due to inertia, so when it is shot upward and falls back down, it does so in a path that keeps it above the flatcar, assuming no external horizontal forces act on it.

Question 19

A projectile is fired over level ground with an initial velocity that has a vertical component of 20 m/s and a horizontal component of 30 m/s.Using g = 10 m/s², the distance from launching to landing points is: A)40 m B)60 m C)80 m D)120 m E)180 m

Accepted Answer

The time of flight can be calculated using the vertical component of the initial velocity and the acceleration due to gravity. The time to reach the maximum height is $t = \frac{v_{vertical}}{g} = \frac{20 m/s}{10 m/s^2} = 2 s$. Since the motion to the maximum height and back down is symmetrical, the total time of flight is $2t = 4 s$. The horizontal distance covered in this time, using the horizontal component of the velocity, is $distance = v_{horizontal} \times time = 30 m/s \times 4 s = 120 m$.

Question 20

A bomber flying in level flight with constant velocity drops a bomb before it is over the target.Neglecting air resistance, which one of the following is NOT true?
A)The bomber is over the target when the bomb strikes
B)The acceleration of the bomb is constant
C)The horizontal velocity of the plane equals the vertical velocity of the bomb when it hits the target
D)The bomb travels in a curved path
E)The time of flight of the bomb is independent of the horizontal speed of the plane

Accepted Answer

The horizontal velocity of the plane will not equal the vertical velocity of the bomb when it hits the target. The horizontal velocity of the bomb will be the same as the horizontal velocity of the plane at the instant of release, but the vertical velocity will change due to the force of gravity. Therefore, the bomb will travel in a curved path and hit the target after the bomber has passed over it. The time of flight of the bomb will depend on both the horizontal and vertical velocities, not just the horizontal speed of the plane.

Quiz 4: Motion in Two and Three Dimensions

A stone thrown from the top of a tall building follows a path that is:

A bullet shot horizontally from a gun:

An airplane is flying north at 500 km/h.It makes a gradual 180 $\degree$ turn at constant speed, changing its direction of travel from north through east to south.The process takes 40 s.The average acceleration of the plane for this turn is:

An airplane makes a gradual 90 $\degree$ turn while flying at a constant speed of 200 m/s.The process takes 20.0 seconds to complete.For this turn the magnitude of the average acceleration of the plane is:

The airplane shown is in level flight at an altitude of 0.50 km and a speed of 150 km/h.At what distance d should it release a heavy bomb to hit the target X? Take g = 10 m/s².

A boy on the edge of a vertical cliff 20 m high throws a stone horizontally outwards with a speed of 20 m/s.It strikes the ground at what horizontal distance from the foot of the cliff? Use g = 10 m/s²

A stone is tied to a string and whirled at constant speed in a horizontal circle.The speed is then doubled without changing the length of the string.Afterward the magnitude of the acceleration of the stone is:

A cannon fires a projectile as shown.The dashed line shows the trajectory in the absence of gravity; points MNOP correspond to the position of the projectile at one second intervals.If g = 10 m/s², the lengths X,Y,Z are:

Two objects are traveling around different circular orbits with constant speed.They both have the same acceleration but object A is traveling twice as fast as object B.The orbit radius for object A is _______ the orbit radius for object B.

A toy racing car moves with constant speed around the circle shown below.When it is at point A its coordinates are x = 0, y = 3m and its velocity is (6 m/s) .When it is at point B its velocity and acceleration are:

An object is moving on a circular path of radius $\pi$ meters at a constant speed of 4.0 m/s.The time required for one revolution is:

A particle moves at constant speed in a circular path.The instantaneous velocity and instantaneous acceleration vectors are:

A stone is thrown outward from the top of a 59.4-m high cliff with an upward velocity component of 19.5 m/s.How long is the stone in the air? Assume that it lands on the ground below the cliff, and that the ground below the cliff is flat.

Two projectiles are in flight at the same time.The acceleration of one relative to the other:

A dart is thrown horizontally toward X at 20 m/s as shown.It hits Y 0.1 s later.The distance XY is:

A large cannon is fired from ground level over level ground at an angle of 30 $\degree$ above the horizontal.The muzzle speed is 980 m/s.Neglecting air resistance, the projectile will travel what horizontal distance before striking the ground?

An object is shot from the back of a railroad flatcar moving at 40 km/h on a straight horizontal road.The launcher is aimed upward, perpendicular to the bed of the flatcar.The object falls:

A projectile is fired over level ground with an initial velocity that has a vertical component of 20 m/s and a horizontal component of 30 m/s.Using g = 10 m/s², the distance from launching to landing points is:

A bomber flying in level flight with constant velocity drops a bomb before it is over the target.Neglecting air resistance, which one of the following is NOT true?

Quiz 4: Motion in Two and Three Dimensions

A stone thrown from the top of a tall building follows a path that is:

A bullet shot horizontally from a gun:

An airplane is flying north at 500 km/h.It makes a gradual 180 °\degree° turn at constant speed, changing its direction of travel from north through east to south.The process takes 40 s.The average acceleration of the plane for this turn is:

An airplane makes a gradual 90 °\degree° turn while flying at a constant speed of 200 m/s.The process takes 20.0 seconds to complete.For this turn the magnitude of the average acceleration of the plane is:

The airplane shown is in level flight at an altitude of 0.50 km and a speed of 150 km/h.At what distance d should it release a heavy bomb to hit the target X? Take g = 10 m/s2.

A boy on the edge of a vertical cliff 20 m high throws a stone horizontally outwards with a speed of 20 m/s.It strikes the ground at what horizontal distance from the foot of the cliff? Use g = 10 m/s2