More 1D kinematics problems

1. Two automobiles drive in the same direction along a snow-covered road. Each moves initially at speed 20 m/s (about 40 mph), and the distance between them is D meters. A deer jumps into the road just 30m (about 100 feet) in front of car B. The driver takes TB to react to the even, after which he slams on the brakes. This car, with good snow tires, decelerates at 2 m/s2.

The driver of the following car, A, doesn't notice the deer, but does see the brake lights of the car in front of him light up. He takes TA to react -- a longer time because this isn't such a dramatic event. When he hits his brake pedal, the older tires decelerate car A at 1.5 m/s2.

1. How far does car B travel before coming to a stop? What is the fate of the deer?
2. How far does car A travel before coming to a stop?
3. How large a distance must there be between cars to prevent a collision?
4. How many "car-lengths" should there be between cars for safety?
5. How many "seconds-of-time" should there be between cars for safety?

2. Joe stands on the edge of the Grand Canyon. He drops a rock over the edge, and listens. Eight seconds later, he hears the faint sound "Plonk".
1. How deep is the Canyon?
2. Suppose that Joe repeats his experiment on the Moon: he drops the rock, then 8 seconds later, feels the vibrations from the impact in his moon boots. The speed of sound through the rock is 2300 m/s. How deep is the lunar canyon?