Problem 1: Two students stand close together at the center of a bridge over a stream about 10 meters below. Simultaneously, the first student (student A) throws a pebble straight down toward the stream with an initial speed of 30 m/s, while the second student (student B) throws a pebble straight up into the air above the stream with an initial speed of 30 m/s. Assume the pebbles were both released at exactly the same instant from exactly 10 m above the stream. Neglect air resistance.
1. What is the velocity of student B's pebble as falls past the point of its release?
2. Just before striking the water, is the velocity of student A's pebble greater than, less than or equal to that of student B?
3. How much time elapses between student A's pebble striking the water and student B's pebble striking the water?
Problem 2: A car travels clockwise once around the track shown below. Starting from rest at point A, the car speeds up at a constant rate until it is just past point C. By the time it reaches point D, it is traveling at a constant speed. It then travels at a constant speed the rest of the way around the track.
1. On the diagram at right, indicate the direction of the acceleration at each of the points D-G. If it is possible to indicate the exact direction of the acceleration, do so, and write "E" for exact. Otherwise, indicate the approximate direction of the acceleration. If the magnitude of the acceleration is zero at any point(s), state so explicitly.
2. Is the magnitude of the acceleration at point G greater than, less than, or equal to that at point D? Explain.
Problem 3: A hiker throws a rock with a velocity of 20 m/s at an angle of 30 degrees above the horizontal into a gorge. The rock hits the water 50 m below the height it was thrown from.
1. What is its maximum height?
2. How long is the rock in the air?
3. How far horizontally does the rock travel?
4. With what velocity (magnitude and direction) does the rock hit the water?