Question

a ball is thrown into the air with an upward velocity of 100 ft/s. its height, h, after t seconds is given by the function h = -16t² + 64t + 960. when did the ball hit the ground? 2 seconds 5 seconds 10 seconds 7 seconds

Explanation:

Step1: Set height to zero

When the ball hits the ground, \( h = 0 \). So we set the equation \( -16t^2 + 64t + 960 = 0 \).

Step2: Simplify the equation

Divide the entire equation by \(-16\) to simplify: \( t^2 - 4t - 60 = 0 \).

Step3: Factor the quadratic

Factor the quadratic equation: \( (t - 10)(t + 6) = 0 \).

Step4: Solve for t

Set each factor equal to zero: \( t - 10 = 0 \) or \( t + 6 = 0 \). This gives \( t = 10 \) or \( t = -6 \). Since time can't be negative, we take \( t = 10 \).

Answer:

10 seconds