Velocity prob: A rock is dropped from a 4oo foot cliff.

[incubar]

I completely forgot how to do these word problems


A rock is dropped from the top of a 4oo foot cliff. Its velocity at time t seconds is v(t)=-32t feet. Please find s(t), the height of the rock above the ground at time t.

b. How Long will the rock in the above problem take to reach the ground?

c. What will the velocity of the rock in the above problem ne when it hits the ground?

 

[arthur ohlsten]

32 has units of " feet per sec squared"


dx/dt =-32t integrate
x=-32t^2/2 +C
x=-16t^2+C
but at t=0 x=400

400 =-16[0]+c
C=400

x=400-16t^2 height of rock at time t answer

when does rock reach the ground?
let x=0
0=400 -16t^2
t^2=400/16 take positive square root
t=20/4
t=5 secs

what is rocks velocity at this time?
dx/dt=-32t
dx/dt=-32[5]
dx/dt=-160 ft per sec answer

Arthur
please check math for errors