Question

help....
A stone is thrown vertically upwards from the edge of a cliff on mars (where the acceleration of gravity is 12ft/s^2) with an initial velocity of 64 ft/s from a heigh of 192 feet above ground. The height of the stone above ground after t seconds iss given by h(t)=-6t^2+64t+192

a. when does the stone reach its highest point? What is the highest point?

B. when does the stone hit the ground? What is it's velocity when it hits the ground?

Answer 1

At highest point final velocity=0
i.e. 64-12t=0
Find t
Now replace this value of t in h(t)=-6t^2+64t+192
That will give you max height!
To find the time when it hits ground put h(t)=0 and solve to find t (say t' to avoid confusion)

the velocity with which it will hit ground will be V=64-12t'
this will give you a negative value but that has nothing much to do since that will only give you direction of velocity!