Vectors
1D Kinematics
Relative Motion
Projectile Motion
100
Soccer player #1 is 8.6 m from the goal (see the drawing). If she kicks the ball directly into the net, the ball has a displacement labeled A. If, on the other hand, she first kicks it to player #2, who then kicks it into the net, the ball undergoes two successive displacements, Ax and Ay. How far is player #2 from both player #1 and the net?
7.45 meters from player #1, 4.3 meters from the net.
100
A pilot flies horizontally at a speed v, at a height h above level ground. However, at time t = 0, the pilot begins to fly over ground sloping upward at angle θ. If the pilot does not change the airplane's heading, find an expression for the time t at which the plane strikes the ground.
t = h/(vtantheta)
100
A river has a steady speed of vs. A student swims upstream a distance d and back to the starting point. If the student can swim at a speed of v in still water, how much time does it take the student to complete the round trip? Express your answer in terms of d, v, and vs.
t = (2d)/(v(1-v_s^2/(v^2)))
100
Which of the three kicks in this figure is in the air for the longest time? They all reach the same maximum height. (a), (b), (c), or d - all the same time.
(d) - all the same time!
200
The drawing shows a triple jump on a checkerboard, starting at the center of square A and ending on the center of square B. Each side of a square measures 4.0 cm. What is the magnitude of the displacement of the colored checker during the triple jump?
25.3 cm.
200
The speed of a bullet is measured to be 640 m/s as the bullet emerges from a barrel of length 1.20 m. Assuming constant acceleration, find the time that the bullet spends in the barrel after it is fired.
3.75 times 10^(-3) s
200
A boat crossing a wide river moves with a speed of 10.0 km/h relative to the water, due north. The water in the river has a uniform speed of 5.00 km/h due east relative to the Earth. If the river is 2.50 km-wide, how far will the boat drift east?
1.25 km east.
200
If a person can jump a maximum horizontal distance (by using a 45° angle) of 3.0 m on Earth, what would be his maximum range on the Moon, where the free-fall acceleration is g/6?
18.0 meters!
300
A person going for a walk follows the path shown in the figure. The total trip consists of four straight-line paths. At the end of the walk, what is the person’s resultant displacement measured from the starting point? Take the +x-axis to be east and the +y-axis to be north.
240 m, 57.2° south of west.
300
A ball is shot vertically upward from the surface of another planet. A plot of height versus time (t = 0 is the time at which the ball is shot) is shown. What are the magnitudes of the free-fall acceleration on the planet AND the initial velocity of the ball?
g = 8.0 m/s^2, v_o = 20 m/s
300
A car travels 10 m/s east. Another car travels 10 m/s north. What is the relative velocity (magnitude and direction, expressed using cardinal directions) of the first car with respect to the second?
14.1 m/s, 45 degrees south of east.
300
A projectile is fired horizontally from the top of a cliff of height h. If the projectile lands a horizontal distance d from the bottom of the cliff, find an expression for the launch speed vo.
v_o = d sqrt(g/(2h)
400
The figure shows three displacement vectors A, B and C. These vectors are arranged in head-to-tail fashion, and they add together to give a resultant displacement R, which lies along the x-axis. What is the magnitude and direction of displacement A?
20.4 m, 59.9° above the +x-axis.
400
As two trains move along a track, their conductors suddenly notice that they are headed toward each other. The figure gives their velocities v as functions of time t as the conductors slow the trains. The figure’s vertical scaling is set by vs = 40.0 m/s. The slowing processes begin when the trains are 200 m apart. What is their separation when both trains have stopped?
d = 40.0 meters.
400
A farm truck moves due east with a constant velocity of 9.50 m/s on a limitless, horizontal stretch of road. A boy riding on the back of the truck throws a can of soda upward, as in the figure, and catches the projectile at the same location on the truck bed, but 16.0 m farther down the road. What is the initial velocity of the can relative to the ground?
12.6 m/s, 41.0° above the horizontal.
400
A firefighter, a distance d from a burning building, directs a stream of water from a fire hose at angle θ above the horizontal, as shown in the figure. If the initial speed of the stream is vi, at what height h does the water strike the building?
h = d tan theta - (gd^2)/(2(v_i)^2cos^2theta