Question

a ball is thrown into the air with an upward velocity of 80 feet per second. the function h = -16t² + 80t models the height h, in feet, of the ball at time t, in seconds. when will the ball reach the ground?
○ after 3 seconds
○ after 4 seconds
○ after 5 seconds
○ after 6 seconds
done

Explanation:

Step1: Set height to 0

When the ball reaches the ground, \( h = 0 \). So we set the equation \( -16t^2 + 80t = 0 \).

Step2: Factor the equation

Factor out \( -16t \) from the left side: \( -16t(t - 5) = 0 \).

Step3: Solve for t

Set each factor equal to zero: \( -16t = 0 \) or \( t - 5 = 0 \). Solving \( -16t = 0 \) gives \( t = 0 \) (initial time when the ball is thrown). Solving \( t - 5 = 0 \) gives \( t = 5 \).

Answer:

after 5 seconds