Problema Solution

An object is launched directly upward at 80 feet per second from a platform 128 feet high. What is the objects height after 1.5 secs? When will it attain its highest height?

Answer provided by our tutors

let


v0 = 80 ft/s initial velocity

a0 = - 32 ft/s^2 acceleration due to gravity

y0 = 128 ft the initial height

t = time in seconds

y = height in ft


y = (1/2)a*t^2 + v0*t + y0


y = - (1/2)32*t^2 + 80*t + 128


y = - 16*t^2 + 80*t + 128


What is the objects height after 1.5 secs?


for t = 1.5 we have


y = - 16*1.5^2 + 80*1.5 + 128


y = 212 ft


When will it attain its highest height?


we need to find t for which the function y has maximum y max


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y max = 128 - 80^2/(4*(-16))


y max = 228 ft


lets find t


- 16*t^2 + 80*t + 128 = 228


by solving we find


t = 2.5 sec


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the object will attain his highest height after 2.5 seconds.