An outfielder throws a baseball to the player on third base. The height h of the ball in feet is modeled by the function h(t) = -16t2 + 19t + 5, where t is time in seconds. The third baseman catches the ball when it is 4 feet above the ground. To the nearest tenth of a second, how long was the ball in the air before it was caught?
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4 = -16t2 + 19t + 5
16t2 - 19t - 1 = 0
solve this for t
zeros of this are 1.23 and - 0.23
t must be positive so the required time is 1.2 seconds
Okay so since its 1.2s can you help me with the next part?
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A player on the opposing team starts running from second base to third base (1.2 s) before the outfielder throws the ball. The distance between the bases is 90 ft, and the runner's average speed is 27 ft/s. Will the runner reach third base before the ball does?
its just yes or no, but im not sure how to work the problem out.
he runs 27 ft in 1 second
so in 1.2 secs he runs 27*1.2 ft= 32.5 ft
as the distance is 90 ft
he won't reach the base in time
i'm assuming the player starts running at same time the first player throws the ball