Susan throws a softball upward into the air at a speed of 32 feet per second from a 104-foot platform. The distance upward that the ball travels is given by the function d(t)=-16t^2+32t+104. What is the maximum height of the softball? How many seconds does it take to reach the ground after first being thrown upward?

When the softball attains maximum height, d(t)/ dt =0
ie  -32t +32 =0

      t=1 s

When t=1, height = -16 (1)^2 +32 (1) +104 =120 feet (shown)

When it reaches the ground, height above ground = 0 ft

ie  -16 t^2 +32t +104 =0

     2t^2 -4t - 13 =0    (dividing both sides by -8)

Hence,  t= 3.74s  (shown)   or  t=-1.74s (rejected)

Hope this helps. Peace.  


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Frederick Koh


I can answer questions concerning calculus, complex numbers, vectors, statistics , algebra and trigonometry for the O level, A level and 1st/2nd year college math/engineering student.


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