Question

A ball is launched into the sky at 54.4 feet per second from a 268.8-meter tall building. The equation for the ball’s height, h, at time t seconds is h = -3.2t^2 + 54.4t + 268.8. When will the ball strike the ground? Please use the quadratic formula in your answer.

a) 4.0 seconds
b) 6.0 seconds
c) 8.0 seconds
d) 10.0 seconds

Answer 1

The ball will strike the ground after 6.0 seconds.

Step-by-step explanation:

To find when the ball will strike the ground, we need to find the value of t when the height, h, is 0. We can do this by setting the equation h = -3.2t^2 + 54.4t + 268.8 equal to 0 and using the quadratic formula: t = (-b +/- sqrt(b^2 - 4ac))/2a. Plugging in the values a = -3.2, b = 54.4, and c = 268.8, we get t = 4.0 seconds or t = 6.0 seconds. Since the ball is launched from a building, we take the longer solution, so the ball will strike the ground after 6.0 seconds.