Aball is launched directly in the air at a speed of 40 feet per second from a platform located 10 feet in the air. the motion of the ball can be modeled using the function f(t)=−16t2+40t+10, where t is the time in seconds and f(t) is the height of the ball. when, in seconds, will the ball hit the ground? write your answer to the nearest hundredth of a second. do not include units in your answer.

The ball will hit the ground in 2.73 s

Explanation:

Hi there!

f(t) is the height of the ball at time "t". We need to find the value of "t" for which f(t) = 0.

f(t) = 0   Then:

-16 · t² + 40 · t + 10 = 0  

Solving the quadratic equation using the quadratic formula (a = -16, b = 40, c = 10):

t = -0.23 s and t = 2.72 s

Since time can´t be negative, be discard that value.

The ball will hit the ground in 2.73 s.

Have a nice day!