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.