Question

Derivatives application of Motion

Velocity and Acceleration...

ex) The velocity 2 ft. below from the starting point is 12 ft, per sec. If the starting point is at height of 56 ft, when and with what velocity does the body strike at the earth?

Answer 1

The height and velocity functions can be written
\[v(t) = -32t + v_{o}\]
\[h(t) = -16t^{2}+v_{o}t + h_{o}\]
where v_o is initial velocity, h_o is initial height
v_o = -12, since body is falling assume negative velocity
h_o = 54, 2 feet from starting point
Basically create new starting point since velocity at old starting point is unknown
Now set h(t) = 0 solve for t
substitute into v(t) to find velocity at impact

Answer 2

i get
t = 1.5 sec
|v| = 60 ft/sec