use a(t) = -32 ft per second squared as the acceleration due to gravity.An object is thrown vertically downward from the top of a 480-ft building with an initial velocity of 64 feet per second. With what velocity does the object hit the ground?

Question

This type of problem always shows up on my test and I always get it wrong. Can someone show me how to do it? Thanks.

Answer 1

At this point you should know that
if s(t) is the height obtained, then
v(t) , or velocity, is s'(t) and
a(t) , the acceleration, is v'(t) or s''(t)

Also having done some of these, by now you should know that for the above,
s(t) = -16t^2 + 64t + 480 and
v(t) = -32t + 64

so when it hits the ground, isn't s(t) = 0 ??
so
-16t^2 + 64t + 480 = 0
t^2 - 4t - 30 = 0
t = 2 ± √34 , we can reject the negative value
t = 2+√34

sub that into v(t) and you are done