Question

Susan throws a softball from the outfield towards home plate. As it flew, its height followed the path of the equation h(t)=−4.9t²+30t+4, where the height h is in feet, and the time t is in seconds. How many seconds will it take the ball to reach the catcher's mitt on the ground at home plate? Round your answer to the nearest whole number.

a. 2 seconds
b. 3 seconds
c. 4 seconds
d. 5 seconds

Answer 1

It will take approximately C)4 seconds for the ball to reach the catcher's mitt on the ground at home plate.

Step-by-step explanation:

The given equation for the height of the softball is h(t) = -4.9t² + 30t + 4. To find the time it takes for the ball to reach the catcher's mitt at home plate, we need to find the value of t when h(t) = 0, since the ball is at ground level at that time.

Setting h(t) = 0, we can solve the quadratic equation -4.9t² + 30t + 4 = 0 to find the value of t. Using the quadratic formula, we find two values for t: t ≈ 0.54 seconds and t ≈ 3.79 seconds. Since the ball is initially thrown upwards before reaching the catcher's mitt, we take the longer time as the correct answer. Therefore, it will take approximately 4 seconds for the ball to reach the catcher's mitt on the ground at home plate.