Ch 2 Homework Name: Follow the instructions on the problems and show your work clearly. 1. (Problem 3) A person travels by car from one city to another with different constant speeds between pairs of cities. She drives for 30.0 min at 80 km/h, 12.0min at 100 km/h, and 45 min at 40.0 km/h and spends 15.0 min eating lunch and buying gas (a) Draw a diagram of the car along the route. (b) Draw velocity versus time graph
(c) Determine the average speed for the trip (d) Plot distance versus time graph. (e) Determine the distance between the initial and final cities along the route.
2. (Problem 10) Two cars travel in the same direction along a straight highway, one at a constant speed of 55 mi/h and the other at 70 mi/h (a) Draw a diagram of the two cars (b) Assuming they start at the same point, how much sooner does the faster car arrive at a destination 10 mi away a. First, define variables b. Solve for the time difference between the cars
(c) How far must the faster car travel before it has a 15-min lead on the slower car a. Use the equation you find in the part (b) and solve for the distance. b. Substitute numbers into the equation and calculate the distance.
3. (Problem 20) A Particle starts from rest and accelerate as shown in the figure below. (a) Determine the particle s speed at t = 10.0s and at t = 20.0 s a. Write down equations you need to use in this part b. Plot velocity versus time graph. c. Determine the particle s speed at t = 10.0s and at t = 20.0 s
(b) Determine the distance traveled in the first 20.0 s a. Write down equations you need to use in this part b. Plot distance versus time graph c. Determine the distance traveled in the first 20.0 s
4. (Problem 22) The average person passes out at an acceleration of 7 g (that is, seven times the gravitational acceleration on Earth, 9.8 m/s 2 ). Suppose a car is designed to accelerate at this rate. How much time would be required for the car to accelerate from rest to 60.0 miles per hour? (The car would need rocket boosters!) (a) Draw a diagram of a car with rocket boosters. (b) Define variables (c) Solve for the time (use variables you define in the part (b)). (d) Substitute numbers into the answer in the part(c)
5. (Problem 29) A truck covers 40.0 m in 8.50 s while uniformly slowing down to a final velocity of 2.80 m/s. (a) Draw a diagram of truck. Using an arrow signs to indicate the direction of the motion and acceleration. (b) Find the truck s original speed (c) Find its acceleration.
6. (Problem 36) A record of travel along a straight path is as follows: 1. Start from rest with a constant acceleration of 2.77 m/s 2 for 15.0s. 2. Maintain a constant velocity for the next 2.05 min. 3. Apply a constant negative acceleration of 9.47 m/s 2 for 4.39s (a) Plot a graph of acceleration versus time. (b) Plot a graph of velocity versus time. (c) What was the total displacement for the trip?
(d) Plot a graph of displacement versus time. (e) What were the average speeds for legs 1, 2 and 3 of the trip, as well as for the complete trip? 7. (Problem 45) A ball is thrown vertically upward with a speed of 25.0 m/s. (a) Draw a diagram of the ball. (b) Define variables
(c) How high does it rise? (Use symbols you define in the part (b) first and substitute numbers at the end.) (d) How long does it take to reach its highest point? (Use symbols you define in the part (b) first and substitute numbers at the end.) (e) How long does the ball take to hit the ground after it reaches its highest point? (Use symbols you define in the part (b) first and substitute numbers at the end.) (f) What is its velocity when it returns to the level from which it started? (Use symbols you define in the part (b) first and substitute numbers at the end.)
8. (Problem 50) A small mailbag is released from a helicopter that is descending steadily at 1.50 m/s. (a) Draw a diagram of the helicopter and mailbag (b) After 2.00 s, what is the speed of the mailbag? a. Define variables. b. Write down an equation you need to use and solve for the speed. c. Substitute numbers into the equation.
(c) After 2.00 s, how far is it below the helicopter?( remember the helicopter is descending steadily and the mailbag is freefalling) a. Define variables. b. Write down an equation you will use and solve for the distance. c. Substitute numbers into the equation.
9. (Problem 60) A student throws a set of keys vertically upward to his fraternity brother, who is in a window a distance h above. The brother s outstretched hand catches the keys on their way up a time t later. (a) Draw a diagram. (b) With what initial velocity were the keys thrown? (c) What was the velocity of the keys just before they were caught?( Answers should be in terms of h, g, and t)
10. (Problem 65) In Chapter 5, we will define the center of mass of an object. The center of mass moves with constant acceleration when constant forces act on the object. A gymnast jumps straight up, with her center of mass moving at 2.80 m/s as she leaves the ground (a) Draw a diagram of a gymnast (b) Define variables and write down a equation you need to use (c) How high above this point is her center of mass at t =0.100s? (d) How high above this point is her center of mass at t =0.200s? (e) How high above this point is her center of mass at t =0.300s? (f) How high above this point is her center of mass at t =0.500s?
(g) Plot a height versus time graph.