
In Example 3, does the rock have a greater speed at t = 1 or t = 3?
Example 3 Motion in a Gravitational Field
Suppose a stone is thrown vertically upward with an initial velocity of 64 ft/s from a bridge 96 ft above a river. By Newton’s laws of motion, the position of the stone (measured as the height above the river) after t seconds is
where s = 0 is the level of the river (Figure 3.45a).
- The position function in Example 3 is derived in Section 6.1. Once again we mention that the graph of the position function is not the path of the stone.
- a. Find the velocity and acceleration functions.
- b. What is the highest point above the river reached by the stone?
- c. With what velocity will the stone strike the river?

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Calculus: Early Transcendentals (3rd Edition)
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