Question

The equation for the motion of a projectile fired straight up at an initial velocity of 64 ft/s is h = 64t - 16t2, where h is the height in feet and t is the time in seconds. Find the time the projectile needs to reach its highest point. How high will it go?

Answer 1

The projectile will reach its highest point when its velocity is zero.
According to equation:
h = 64t - 16t²

Differentiating it with respect to t we get the velocity.
dh/dt = v = 64 - 32t

For max. h, v must be zero.
therefore t = 64/32
= 2sec
putting it in h = 64t - 16t²
we get
h=64(2)-16(2)²
=64 ft

So time = 2sec
and height = 64 ft