Collected Problems for Test 1

Problem #1 (Due 1/20 Friday by 2:00 p.m.)
In a relay race, each contestant runs 25.0 m while carrying an egg balanced on a spoon, turns around, and comes back to the starting point. Jarrow runs the first 25.0 m in 20.0s. On the return trip he is more confident and takes only 15.0s.
a) Sketch a position vs. time graph.
b) What is the magnitude of his average velocity for the first 25.0 m?
c) What is the magnitude of his average velocity for the return trip?
d) What is his average velocity for the entire round trip?
e) What is his average speed for the round trip?

Problem #2 (Due 1/25 Wednesday by 2:00 p.m.)
A sled starts from rest at the top of a hill and slides down with a constant acceleration. At some later time it is 14.4 m from the top; 2.00 s after that it is 25.6 m from the top, 2.00 s later 40.0 m from the top, and 2.00 s later it is 57.6 m from the top.
a) Sketch a position vs. time graph showing the data above on the graph.
b) What is the magnitude of the average velocity of the sled during each of the 2.00 s intervals after passing the 14.4 m point?
c) What is the acceleration of the sled?
d) What is the speed of the sled when it passes the 14.4 m point?
e) How much time did it take to go from the top to the 14.4 m point?
f) How far did the sled go during the first second after passing the 14.4 m point?

Problem #3 (Due 1/26 Thursday by 2:00 p.m.)
As soon as a traffic light turns green, a car speeds up from rest with a constant acceleration of 4.02 m/s². In the adjoining bike lane, a cyclist speeds up from rest to 8.94 m/s with a constant acceleration of 5.81 m/s². The cyclist maintains a constant velocity after reaching its cruising speed while the car is still accelerating at 4.02 m/s² when it passes the bike.
a) Sketch a position vs. time graph. Put both the car and bike on the same graph and make sure you label them. Be neat.
b) Sketch a velocity vs. time graph.
c) Determine the time it takes for the bike to get up to its cruising speed and the position it is at when it reaches this speed.
d) Determine the final position and the total time elapsed until the car catches up to the bike.

Problem #4 (Due 1/27 Friday by 2:00 p.m.)
You are climbing in the High Sierra where you suddenly find yourself at the edge of a fog-shrouded cliff. To find the height of this cliff, you drop a rock from the top and 10.0 s later hear the sound of it hitting the ground at the foot of the cliff.
a) Sketch a position vs. time graph for the 10.0 seconds that goes by. Indicate both the rock and sound on the graph.
b) Ignoring air resistance, how high is the cliff if the speed of sound is 330 m/s?
c) Suppose you had ignored the time it takes the sound to reach you. In that case, would you have overestimated or underestimated the height of the cliff? Explain your reasoning.

Problem #5 (Due 2/1 Wednesday by 2:00 p.m.)
An airplane starting from airport A flies 301 km east, then 352 km at 30.0^o west of north, and then 153 km north to arrive finally at airport B.
a) The next day, another plane flies directly from A to B in a straight line. In what direction should the pilot travel in this direct flight?
b) How far will the pilot travel in flight?

Problem #6 (Due 2/2 Thursday by 2:00 p.m.)
A bird flies in the xy-plane with a velocity vector given by v = (A - Bt²) i + Ct j, with A = 2.4 m/s, B = 1.6 m/s³, and C = 4.0 m/s². The positive y-direction is vertically upward. At t = 0 the bird is at the origin.
a) Calculate the position and acceleration vectors of the bird as functions of time.
b) What is the bird's altitude (y-coordinate) as it flies over x = 0 for the first time after t = 0?

Problem #7 (Due 2/3 Friday by 2:00 p.m.)
#8. The Essex county sheriff is trying to determine the speed of a car that slid off a small bridge on a snowy New England night and landed in a snow pile 4.00 m below the level of the road. The tire tracks in the snow show that the car landed 12.0 m measured horizontally from the bridge.
a) Sketch a y vs. x graph.
b) How fast was the car going when it left the road?
c) How fast was the car going when it hit the ground and at what angle did it hit the ground relative to horizontal?

Problem #8 (Due 2/6 Monday by 2:00 p.m.)
A 2.7 kg ball is thrown upward with an initial speed of 20.0 m/s from the edge of a 45.0 m high cliff. At the instant the ball is thrown, a woman starts running away from the base of the cliff with a constant speed of 6.00 m/s. The woman runs in a straight line on level ground, and air resistance acting on the ball can be ignored.
a) Sketch a y vs. x graph for the ball as viewed by a person at rest on the ground.
b) At what angle above the horizontal should the ball be thrown so that the runner will catch it just before it hits the ground?
c) Sketch a y vs. x graph for the ball as viewed by the runner.
d) How far does the woman run before she catches the ball?