**Assignment4**

A diver of mass 75 kg jumps upward off a diving board and into the water.

**Question 2**

A diver of mass 75 kg jumps upward off a diving board and into the water. The diving board is 2 m above the water.

When the diver jumps, she has a speed of 2.5 m/s. How much kinetic energy does she have?

How much gravitational potential energy will she have gained at her highest point?

Explain how you found the answer.

Based on the diver’s speed from part (a), how high above the board will she rise?

How fast will the diver be moving when she hits the water?

**Question 3**

At the beginning of a bobsled race, teammates push their bobsled along the track before jumping into it.

Before the teammates jump in, they push the bobsled (m = 100 kg) from rest to a speed of 6 m/s. How much kinetic energy does the bobsled gain?

How much work did the bobsled team do? Explain how you found the answer.

If the teammates pushed the bobsled a distance of 8 m, how much force did they apply?

Later, the bobsled is racing down the track at a speed of 20 m/s. With the team in it, the bobsled has a total mass of 325 kg. How much work must be done by friction to slow down the bobsled to 17 m/s?

**Question 4**

The coordinate plane below shows the path of a bicyclist. Each square represents 10 meters.

What is the displacement of the cyclist?

What is the distance traveled by the cyclist?

If the whole trip takes 30 seconds, what is the average speed of the cyclist?

If the whole trip takes 30 seconds, what is the average velocity of the cyclist?

Between points A and B, the cyclist increases his speed from 2 m/s to 5 m/s in a time of 2 seconds. What is the magnitude of his acceleration?

**Question 5**

You stand on a bridge above a river and drop a rock into the water below from a height of 53m.

What is the acceleration of the rock as it falls?

How long does it take to hit the water?

How much more time would it take if instead of dropping the rock straight down, you threw it horizontally with a speed of 5 m/s? Explain.

You throw another rock at an angle of 30° above the horizontal with a speed of 12 m/s.

What are the x- and y-components of the rock’s speed?

How long does it take the rock to reach its maximum height?

**Question 6**

April is moving into a new apartment. She is moving a box of books that has a mass of 30kg.

What is the weight of the box?

What is the normal force acting on the box when it sits on the floor? Explain how you found the answer.

If she pushes on the box with a force of 100 N and there is no friction, what is the acceleration of the box?

If the coefficient of static friction between the box and the floor is 0.3, what is the maximum force of static friction acting on the box?

How hard must she push on the box to get it to slide?

If she pushes on the box with a force of 100 N, and the coefficient of kinetic friction is 0.25, what is the net force on the box in the x-direction?

Based on your answer to part (f), what is the acceleration of the box?

**Question 7**

A car of mass 1250 kg drives around a curve with a speed of 22 m/s.

If the radius of the curve is 35 m, what is the centripetal acceleration of the car?

The maximum friction that the car’s tires can apply is 20,000 N. What is the radius of the smallest circle the car can drive in at a speed of 22 m/s?

**Question 8**

Alan hits a hockey puck of mass 0.3 kg across a hockey rink with a speed of 23 m/s to the south.

What is the momentum of the hockey puck?

If the puck started at rest and the time of impact was 0.1 seconds, what force did Alan apply to the puck when he hit it?

The puck slides across the rink, losing 2 m/s of speed due to friction. What impulse is applied by friction?

When Alan’s puck is moving at 21 m/s south, it collides with an ice skate of mass 2 kg sitting on the rink. Alan’s puck bounces backward at a speed of 4 m/s. What is the

momentum of the puck-skate system before the collision?

What is the speed of the ice skate after the collision?

**Question 9**

A toy dart gun uses a spring with a spring constant of 35 N/m. To use the dart gun, you compress the spring by pushing in a dart of mass 0.002 kg.

If you compress the spring by 0.02 m, what force is the spring exerting on the dart?

With the spring compressed 0.02 m, how much elastic potential energy is stored in the spring?

If you release the spring, it pushes the dart forward. What is the kinetic energy of the dart when it reaches the natural length of the spring? Explain how you found the answer.

What is the speed of the dart when it reaches the natural length of the spring?