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
click here to see the graph of the function
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
click here to see the step by step solution of the equation
the object will attain his highest height after 2.5 seconds.