Motion in two dimensions: projectile and circular motion.

1.) An astronaut shipwrecked on a distant planet with unknown characteristics is on top of a cliff, which he wishes to descend. He does not know the acceleration due to gravity on the planet, and he has only a good watch with which to make measurements. He wants to learn the height of the cliff, and to do this, he makes two measurements. First, he lets a rock fall from rest off the cliff edge; he finds that the rock takes 4.15 s to reach the distant ground.Second, he releases the rock from the same spot but tosses it upward so that it rises a height of what he estimates to be 2 m before it falls to the ground below. This time the rock takes 6.30 s to reach the ground. What is the height of the cliff?

2.) A lifeguard standing on a tower throws a buoy to a swimmer 5 m from the tower. The lifeguard, positioned 3 m above he water, pulls int he rope at a speed of 1 m/s. How fast is the swimmer coming to the shore when he is (a) 4 m and (b) 3 m from the water's edge?

3.) A punter kicks a football during a critical football game. The ball leaves his foot from ground level with a speed of 28 m/s at an angle of 50 degrees to the horizontal. At the very top of its flight, the ball hits a wandering seagull. The ball and the seagull each stop dead and fall vertically from the point of collision. In the following, ignore air resistance. (a) With what speed is the ball moving when it strikes the seagull? (b) How high was the unfortunate seagull when it met the ball? (c) What is the speed of the seagull when it hits the ground?

4.) You must throw a baseball to hit a target on the ground 50 m from the base of a building that is 20 m in height. You are standing at a point on the edge of the roof nearest the target. (a) With what velocity must you throw the baseball if it is to leave the hand horizontally? (b) With what velocity must you throw the baseball if it is to leave the hand at an angle of 45 degrees up from the horizontal? (c) What is the horizontal component of the initial value of the velocity in case (b) ?

5.) A mass is tethered to a post and moves in a circular path of radius r = 0.35 m on an air table - friction free- at a constant speed v = 18 m/s. (a) If at t = 0 s the mass is at theta = 0 degrees, what are the coordinates (x,y) of the mass at t = 0.1 s? (b) What is the acceleration vector of the mass at t = 0 s? (c) What is the acceleration vector of the mass when theta = 90 degrees?