ASTR120 HOMEWORK # 1

1) Calculate the energy associated with a 3000 pound car traveling at a velocity of 55 miles per hour. Remember that

$$Energy \; = \; {1 \over 2 } \; m \; v^2$$

where m is the mass of the car and v is the velocity. Give your answer in Joules.

2) Compare the momentum imparted to you by a baseball compared to a person walking into you.

$${\rm Momentum \; = \; m \; v }$$

Assume that the baseball is moving at 70 miles per hour and has a mass of 160 grams. Make reasonable estimates for the mass and velocity of a walking person. Why would the baseball hurt more?

3) Calculate how long it takes light to travel from a flashlight in your hand on the surface of the Earth to the Moon. Remember the formula is

$$distance \; = \; velocity \; \times \; time$$

express your answer in minutes. How different would your answer be if the Moon were just rising or just setting when you shined your light? Draw a picture and calculate the difference.

4) You are in your car and the light changes to green. From a standing stop, you put the petal-to-the-metal, accelerating at a constant rate of 19.6 meters per second² (that's 2-g's so you are pinned to the back of the seat - probably a jet powered car). For a constant rate of acceleration, your velocity and distance are given by

$$Velocity \; = \; acceleration \; \times \; time$$

$$Distance \; = \; {1 \over 2} \; acceleration \; \times \; time^2$$

What is your velocity in miles/hour when you are 1 mile from the starting point? How long does it take you to get there?

(Problem 5 is on the backside)

5) Conservation of momemtum is one of the big physical laws. It says that the momentum (mass x velocity) of a system must be conserved.

$$M_1 \; V_1 \; + \; M_2 \; V_2 \; = \; constant \; with \; time$$

where M₁ and V₁ are the mass and velocity of one part of the system and M₂ and V₂ are the mass and velocity of another part.

Let's use this law to think about a rocket sitting in space, nothing around it, no velocity; it's momentum is zero. The rocket can accelerate by turning on its engine and firing hot exhaust gas out the backend. Assuming that the exhaust leaves the engine at 3000 miles per hour, and the total rocket plus fuel has a mass of 20,000 kilograms at the start, how much of a payload can you get going at a speed of 0.1 times the speed of light?