Physics MOTION ALONG A STRAIGHT LINE

Physics MOTION ALONG A STRAIGHT LINE
1. A car moving at 20 m/s decelerates at 1.0 m/s² until its speed is 10 m/s. For how long must it decelerate, and how far will it travel in this time?

2. A skier at a NM resort going 20 mph loses control and runs into a tree, head-first.

(a) If her helmet crumples a distance of 1.5 inches, what is the deceleration of her head? (Express your answer in multiples of g – called “g’s”.)

(b) What would have been the deceleration (in g’s) if she hadn’t been wearing a helmet? Assume constant deceleration,

and for part (b) assume that without a helmet her head crumples 0.5 inches.

3. At the Empire State Building, an express elevator carries tourists to the observation deck at a speed of 10 m/s. As they pass the 83rd floor the cable brakes are applied, and the elevator decelerates at 12 m/s².

(a) How many meters past the 83rd floor will the elevator travel before it stops? At this rate of deceleration, passengers experience a brief moment of weightlessness and float up into the air.Their fun comes to an unfortunate end when they crash back down onto the elevator floor.

(b) What is the maximum height that they reach above the floor of the elevator?

(c) When they return to the floor, with what speed do they make contact?

4. A car turns down a narrow dark ally in Boston, and the driver steps on the gas, accelerating from rest at a rate of 2.0 m/s/s. A pedestrian standing in the ally 25 meters from the car starts running away at a constant speed, hoping to make it to the other end, 75 meters away, before he is run over. How fast must he run to escape with his life?

5. In the 1991 World Track and Field Championships in Tokyo, Mike Powell jumped 8.95 m, breaking the 23-year old long-jump record set by Bob Beamon in Mexico City. Assuming that g=9.80 m/s/s in Tokyo, what is the slowest possible launch-speed that would allow Beamon to travel that distance?

6. A WHAM-O superball is dropped from rest from an initial height of 2.0 m. It bounces and returns to a maximum height of 1.80 m.

(a) How long does this take?

((( The superball continues to bounce, as superballs are prone to do, each time returning to a new maximum height that is 9/10 of its maximum height on the previous bounce. )))

(b) How high will it go after its 5th bounce?

(c) How much time will it take for the ball to stop bouncing completely, and how many bounces will it make before it stops?

7. A football can be kicked at an initial speed of 25 m/s. What are the (a) least and (b) greatest elevation angles at which the football can be kicked to score a field goal from a point 50 m in front of the goalposts whose cross-bar is 3.44 m above the ground?
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