(1) A ball is thrown horizontally from a height of 20.8m and hits the ground with a speed that is three times its initial speed. What was the initial speed?

(2) A ball is shot from the ground into the air. At a height of 9.1m, the velocity is observed to be V = 7.9i + 5.1j in m/s (i horizontally, j upward). To what maximum height will the ball rise?

(b) What is the velocity of the ball the instant before it hits the ground? That is its i component.

(c) What is the j component?

3. A light plane attains an air speed of 390 km/h. The pilot sets a course for a destination 800km to the north but discovers that the plane must be headed 10 degrees east of north to fly there directly. The plane arrives in 1.86 hours. What was the i component of the wind velocity vector in km/h?

(b) What was the j component of the wind velocity vector?

Solution Preview

1. Using the energy method, assume the initial speed is v, and then from the energy method, we can get:

mgh + 1.2mv^2 = 1/2m(3v)^2

9.8*20.8 = 4v^2

We got, v = 7.1 m/s

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