Problema Solution
Tom threw a ball upwards while standing on a platform 35 ft above ground. The height after t seconds follows the equation: h(t)=-.7t^2+84t+35. What will be max height of ball and how long will it take to reach max height?
Answer provided by our tutors
we need to find the maximum value of the parabolic function h(t)=-.7t^2+84t+35
h max = c - b^2/(4a), where a = - 0.7, b = 84, c = 35
h max = 35 - 84^2/(4*(-0.7))
h max = 2,555 ft is the max height
now lets find t max so that h (t max) = 2555
-0.7t^2+84t+35 = 2555
-0.7t^2+84t-2520 = 0 divide both sides by -0.7
t^2-120t+3600= 0
by solving we find
t = 60 sec
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the ball will reach max height after 60 seconds.