A ball is thrown upward from the top of a building. The... | SAT Nonlinear functions Question, Answer Explained

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A ball is thrown upward from the top of a building. The ball's height above the ground, in meters, $t$ seconds after it is thrown is modeled by $h(t) = -4.9t^2 + 19.6t + 24.5$ . How many seconds after it is thrown does the ball hit the ground?

$1$

$2$

$4$

$5$

Show answer and explanation

Answer: D

The ball hits the ground when $h(t) = 0$ . Divide $-4.9t^2 + 19.6t + 24.5 = 0$ by $-4.9$ : $t^2 - 4t - 5 = 0$ . Factor: $(t - 5)(t + 1) = 0$ , so $t = 5$ or $t = -1$ . Time after the throw can't be negative, so $t = 5$ seconds.

Choice C is when the ball comes back down to its starting height, $24.5$ meters, not when it reaches the ground.

Why the other choices are wrong

A. This comes from factoring t² - 4t - 5 as (t + 5)(t - 1), which has the signs reversed.
B. At 2 seconds the ball is at its maximum height, 44.1 meters above the ground.
C. At 4 seconds, h(t) = 24.5, so the ball is back at the height of the building's top, not at the ground.

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