4A two dimensional kinematics homework set 2.

1. Find the initial launch angle such that the maximum height of a projectile is equal to its horizontal range.

2. Car A is traveling east at 20 m/s at constant velocity. As car A crosses the intersection shown in the diagram, car B starts from rest 40m north of the intersection and moves south with a constant acceleration of 2 m/s².



  a. What is the position of B relative to A 6 s after A crosses the intersection?
  b. What is the velocity of B rlative to A for t = 6 s?
  c. What is the acceleration of B relatvie to A for t = 6 s?

3. A freight train is moving at a constant speed of 10 m/s. A man standing on a flatcar throws a ball into the air and catches it as it falls. Relative to the flatcar, the initial vellocity of the ball is 15 m/s straight up.
   a. What are the magnitude and direction of the initial velocity of the ball as seen by a second man standing on the ground next to the track?
   b. How much time is the ball in the air according to the man on the train? According to the man on the ground? Mathematical prove your two answers.
   c. What horizontal distance has the ball traveleed by the time it is caught according to the man on the train? According to the man on the ground?
   d. What is the minimum speed of the ball during its flight according to the man on the train? According to the man on the ground?
   e. What is the acceleration of the ball according to the man on the train? According to the man on the ground?

4. Galileo, in his Two New Sciences, states that "for elevations (angles of projection) which exceed or fall short of 45 degrees by equal amounts, the ranges are equal. Prove it.

5. A rifle with a muzzle velocity of 1500 ft/s shoots a bullet at a target 150 ft away. How high above the target must the rifle be aimed so that the bullet will hit the target?

6. A bus with a vertical windshiled moves along in a rainstorm at speed V relative to the ground. The raindrops fall vertically with a terminal speed of V' relative to the ground. At what angle do the raindrops strike the windshield?

7. Mathematically prove that the maximum range of a projectile occurs when it is fired at 45 degrees above the horizontal.

8. A jetliner with an airspeed of 1000 km/hr sets out on a 1500 km flight due south. To maintain a southward direction, however, the plane must be pointed fifteen degrees west of south. If the flight takes 100 min, what is the wind velocity?

9. A man can row a boat at 4 m/s in still water. The current in a river is 2 m/s. The river is 40 m wide. If he wants to cross the river in the smallest possible time at what direction should he aim the boat?