Problem 1: A ball is thrown horizontally from the top of a 95 m building and lan

Question

Problem 1: A ball is thrown horizontally from the top of a 95 m building and lands 150 m from the base of the building. Ignore air resistance, and use a coordinate system whose origin is at the top of the building, with positive y upwards and positive x in the direction of the throw.

Part (a) How long is the ball in the air in seconds?

Part (b) What must have been the initial horizontal component of the velocity in m/s?

Part (c) What is the vertical component of the velocity just before the ball hits the ground in m/s?

Part (d) What is the magnitude of the velocity of the ball just before it hits the ground in m/s?

Problem 2: An athlete crosses a 28 m wide river by swimming perpendicular to the water current at a speed of 0.8 m/s relative to the water. He reaches the opposite side at a distance 42 m downstream from his starting point.

Part (a) How fast is the water in the river flowing with respect to the ground in m/s?

Part (b) What is the speed of the swimmer with respect to a friend at rest on the ground in m/s?

Explanation / Answer

1)

Drop time = sqrt.(2h/g) = 4.403 secs. (g = 9.8).
Vertical component of V at ground = sqrt.(2gh) = 43.150m/sec.
Horizontal V component = (150/4.403) = 34.067m/sec.
V at ground = sqrt.(43.150^2 + 34.067^2) = 54.977m/sec., and direction = arctan (34.067/43.150) = 38.29

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