Problema Solution
a firework is shot upward with an initial velocity of 96 feet per second from atop a 200ft tall tower. The firework will explode once it reaches max height. When will the firework reach its max height?
Answer provided by our tutors
let
v = 96 ft/s the initial velocity
h0 = 200 ft the initial height
g = 32 ft/s^2 gravitational acceleration
t = the time of the travel
h(t) = h0 + vt - (1/2)gt^2
h(t) = 200 + 96t - (1/2)32*t^2
we need to find t such that t >0 and h(t) = 0 that is:
200 + 96t - (1/2)32*t^2 = 0
by solving we find:
t = 7.64 s
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the firework will reach its max height in 7.64 seconds.