Chapter 3.6, Problem 4QC

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

     $s\left(t\right)=-16t^2+64t+96,$

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.

1. a. Find the velocity and acceleration functions.
2. b. What is the highest point above the river reached by the stone?
3. c. With what velocity will the stone strike the river?