Problema Solution

Susan throws a softball upward into the air at a speed of 32 feet per second from a 120 dash foot120-foot platform. The distance upward that the ball travels is given by the function d left parenthesis t right parenthesis equals negative 16 t squared plus 32 t plus 120d(t)=−16t2+32t+120. What is the maximum height of the​ softball? How many seconds does it take to reach the ground after first being thrown​ upward? ​ (Round your answer to the nearest​ tenth.)

Answer provided by our tutors

We need to find the maximum of the parabolic function:

d(t)=−16t^2+32t+120

d max = c - b^2/4a, where a = -16, b = 32, c = 120

d max = 120 - 32^2/(4*(-16))

d max = 136 ft

The maximum height of the softball is 136 feet.

The softball will reach the ground after t seconds (t >0) when d(t) = 0

−16t^2+32t+120 = 0 

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click here to see the equation solved for t

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t = 3.92 sec

The softball will reach the ground after 3.92 seconds.