EXAMPLE 6 Solve a multi-step problem An athlete throws a shot put with an initial vertical velocity of 40 feet per second as shown. a. Write an equation.

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EXAMPLE 6 Solve a multi-step problem An athlete throws a shot put with an initial vertical velocity of 40 feet per second as shown. a. Write an equation that models the height h (in feet) of the shot put as a function of the time t (in seconds) after it is thrown. b. Use the equation to find the time that the shot put is in the air. SPORTS

Solve a multi-step problem EXAMPLE 6 a. Use the initial vertical velocity and the release height to write a vertical motion model. h = – 16t 2 + vt + s Vertical motion model h = – 16t t Substitute 40 for v and 6.5 for s. b. The shot put lands when h = 0. To find the time t when h = 0, solve 0 = – 16t t for t. To solve the equation, graph the related function h = – 16t t on a graphing calculator. Use the trace feature to find the t -intercepts.

Solve a multi-step problem EXAMPLE 6 ANSWER There is only one positive t -intercept. The shot put is in the air for about 2.6 seconds.

GUIDED PRACTICE for Example 6 WHAT IF? In Example 6, suppose the initial vertical velocity is 30 feet per second. Find the time that the shot put is in the air. 6. ANSWER About 2.1 seconds