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Kinematics in 2-D (496765)
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About this Assignment
Due: Fri Aug 31 2007 02:59 AM MDT
1. CJ6 3.P.006. [294522] Show Details
In a football game a kicker attempts a field goal. The ball remains in contact with the kicker's foot
for 0.050 s, during which time it experiences an acceleration of 340 m/s2. The ball is launched at
an angle of 55° above the ground. Determine the horizontal and vertical components of the launch
velocity.
vx =
[9.75] m/s
vy =
[13.9] m/s
2. CJ6 3.P.007. [239452] Show Details
A dolphin leaps out of the water at an angle of 35° above the horizontal. The horizontal
component of the dolphin's velocity is 6.5 m/s. Find the magnitude of the vertical component of the
velocity.
[4.55] m/s
3. CJ6 3.P.016. [239455] Show Details
A rock climber throws a small first aid kit to another climber who is higher up the mountain. The
initial velocity of the kit is 24 m/s at an angle of 57° above the horizontal. At the instant when the
kit is caught, it is traveling horizontally, so its vertical speed is zero. What is the vertical height
between the two climbers?
[20.7] m
4. CJ6 3.P.022. [239456] Show Details
A car drives straight off the edge of a cliff that is 57 m high. The police at the scene of the accident
note that the point of impact is 140 m from the base of the cliff. How fast was the car traveling
when it went over the cliff?
[41] m/s
5. CJ6 3.P.031. [239459] Show Details
A horizontal rifle is fired at a bull's-eye. The muzzle speed of the bullet is 685 m/s. The barrel is
pointed directly at the center of the bull's-eye, but the bullet strikes the target 0.023 m below the
center. What is the horizontal distance between the end of the rifle and the bull's-eye?
[46.9] m
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6. CJ6 3.P.071. [239475] Show Details
An airplane is flying with a velocity of v0 = 234 m/s at an angle of 30.0° with the horizontal, as the
drawing shows. When the altitude of the plane is h = 2.2 km, a flare is released from the plane.
The flare hits the target on the ground. What is the angle ?
[41.2]°
7. CJ6 3.CQ.002. [310906] Show Details
An object is thrown upward at an angle
above the ground, eventually returning to earth.
(a) Is there any place along the trajectory where the velocity and acceleration are
perpendicular? If so, where?
(_) at the initial position of motion
(o) at the highest point in the trajectory
(_) at the final position of motion
(_) velocity and acceleration are never perpendicular
Explain.
Key: An object thrown upward at an angle will follow the trajectory shown below. Its
acceleration is that due to gravity, and therefore, always points downward. The acceleration is
denoted by a y in the figure. In general, the velocity of the object has two components of the
velocity, vx and v y. Since a x = 0, vx always equals its initial value. The y component of the
velocity, vy, decreases as the object rises, drops to zero when the object is at its higher point, and
then increases in magnitude as the object falls downward.
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Since vy = 0 when the object is at the highest point, the velocity of the object points only in the x
direction. As suggested in the figure above, the acceleration will be perpendicular to the velocity
when the object is at its highest point and vy = 0.
(b) Is there any place where the velocity and acceleration are parallel? If so, where?
(_) at the initial position of motion
(_) at the highest point in the trajectory
(_) at the final position of motion
(o) velocity and acceleration are never parallel
Explain.
Key: In order for the velocity and acceleration to be parallel, the x
component of the velocity would have to drop to zero. However, vx always
remains equal to its initial value; therefore, the velocity and acceleration can
never be parallel.
8. CJ6 3.CQ.003. [311033] Show Details
Is the acceleration of a projectile equal to zero when it reaches the top of its trajectory?
(_) yes
(o) no
(_) not enough information to decide
Why or why not?
Key: As long as air resistance is negligible, the acceleration of a projectile is constant
and equal to the acceleration due to gravity. The acceleration of the projectile,
therefore, is the same at every point in its trajectory, and can never be zero.
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9. CJ6 3.CQ.010. [310916] Show Details
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A stone is thrown horizontally from the top of a cliff and eventually hits the ground below. A second
stone is dropped from rest from the same cliff, falls through the same height, and also hits the
ground below. Ignore air resistance. Discuss whether each of the following quantities is different or
the same in the two cases.
(a) displacement
(o) displacment is greater for stone that is thrown horizontally
(_) displacment is greater for stone that is thrown vertically
(_) displacment is equal in each case
Explain.
Key: The displacement is greater for the stone that is thrown horizontally,
because it has the same vertical component as the dropped stone and, in
addition, has a horizontal component.
(b) speed just before impact with the ground
(o) speed before impact is greater for stone that is thrown horizontally
(_) speed before impact is greater for stone that is thrown vertically
(_) speed before impact is equal in each case
Explain.
Key: The impact speed is greater for the stone that is thrown horizontally.
The reason is that it has the same vertical velocity component as the
dropped stone but, in addition, also has a horizontal component that equals
the throwing velocity.
(c) time of flight
(_) time of flight is greater for stone that is thrown horizontally
(_) time of flight is greater for stone that is thrown vertically
(o) time of flight is equal in each case
Explain.
Key: The time of flight is the same in each case, because the vertical part of
the motion for each stone is the same. That is, each stone has an initial
velocity component of zero and falls through the same height.
Submit for Testing
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