Mathematics

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2. The graph in Figure 1.24 shows the distance versus time for an elevator as it moves up and down in a building. Compute the elevator’s

velocity at the times marked a, b,and c. (This is problem 14 of chapter 1.) 6pts

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Figure 1.24

3. During takeoff, an airplane goes from 0 to 50 m/s in 8 s.
a) What is its acceleration? 6pts
b) How fast is it going after 5 s? 6pts
c) How far has it traveled by the time it reaches 50 m/s? 6pts
(This is Problem 28 of chapter 1.)

4. As a baseball is being caught, its speed goes from 30 to 0 m/s in about 0.005 s. Its mass is 0.145 kg.
a) What is the baseball’s acceleration in m/s² and in g’s? 7pts
b) What is the size of the force acting on it? 6pts
(This is Problem 14 of chapter 2.)

5. The biggest asteroid (Asteroid 2005 YU55 400 m wide) to cruise by the Earth in 35 years made its closest approach on Tuesday November

11/08/2011 at 6:28 p.m. (PST). According to NASA, at the point of closest approach, it was no closer than 324,600 km from the center of

the earth. Let us assume that Asteroid 2005 YU55 has a mass of 10 billion kg.
a) Calculate the gravitational force of attraction between the asteroid and the earth at the point of closest approach. (Use

5.98×10^24 kg for the mass of the earth.) 6pts
b) Assume that the asteroid goes into circular orbit at a distance of 324,600 km from the center of the earth. Find the

acceleration and speed of the asteroid in its circular orbit. 6pts

6. A running back with a mass of 80 kg and a speed of 8m/s collides with, and is held by, a 120-kg defensive tackle going in the opposite

direction. How fast must the tackle be going before the collision for their speed afterward to be zero? 10pts
(This is Problem 10 of chapter 3.)

7. As it orbits the Earth, the 11,000-kg Hubble Space Telescope travels at a speed of 7,900 m/s and is 560,000m above the Earth’s surface.
a) What is its kinetic energy? 6pts
b) What is its potential energy? 6pts
(This is Problem 16 of chapter 3.)

8. The fastest that a human has run is about 12 m/s.
a) If a pole vaulter could run this fast and convert all of his or her kinetic energy into gravitational potential energy, how high

would he or she go? 7pts
b) Using the 1990 pole vault world record of 20 ft. Find the initial speed in m/s needed for the pole vaulter to reach this height.

6pts
(This is Problem 24 of chapter 3.)

9. a) A 3,000-kg truck runs into the rear of a 1,000-kg car that was stationary. The truck and car are locked together after the

collision and move with speed 9 m/s. What was the speed of the truck before the collision? (This is Problem 6 of chapter 3.) 6pts
b) Compute how much kinetic energy was “lost” in the collision in part (a). (This is Problem 28 of chapter 3.) 6pts

10. An elevator is able to raise a 1,000 kg mass to a height of 40 m in 15 s
a) How much work does the elevator do? 7 pts
b) What is the elevator’s power output? 7 pts
c) What is the change in the potential energy of the elevator