Question

An object is dropped from a 400-ft tower.

a) when does it hit the ground?

b) how fast is it going at the time of impact?

Answer 1

the acceleration due to gravity is 32 ft/s^2. \[a(t)=f^{''}(t)=-32\]
\[v(t)=f^{'}(t)=-32t+c\]
\[d(t)=f(t)=-16t^2+ct+k\]
given we are dropping the object from a height of 400ft \[v(0)=0 \rightarrow c=0; d(0)=400 \rightarrow k=400\]
\[v(t)=-32t; d(t)=400-16t^2\]
when it hits the ground:
\[0=400-16t^2; t=\pm5\]
although -5 is technically true it does not make sense in the problem
\[t=5 \rightarrow v(5)=-160\]
so
a)= 5 seconds
b)= -160 ft/s