How do I calculate the velocity at impact in projectile motion?

[j_sun]

For example, my position function is s(t) = -16t^2 + 96t

My velocity function is s'(t) = -32t^2+96

Can someone show me please?

Also, does the unit of measurement change after I take the derivative? Thanks!

[Sandstorm]

Your second line has an error. s' = -32t + 96.

Solve s = -16t^2 + 96t = 0 to find the time of impact. (Obviously not the t = 0 solution.)

Substitute this value of t into the velocity function.

Units of velocity are distance/time e.g. ft/sec.

[Melanie]

s(t) = -16t^2 + 96t

Find the time when the object lands on the ground. It lands on the ground when s = 0.

0 = -16t^2 + 96t

0 = t(-16t + 96)

t = 0

or

-16t + 96 = 0

t = 6

============
s = -16t^2 + 96t

v = -32t + 96

v(6) = -32(6) + 96 = -96

So the velocity at impact is 96.

Note that velocity is negative because the object is falling down.

Remember that velocity represents direction AND speed.