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

if you wrote this as
\[ y = -16x^2 + 64 x \]
do you notice it is a parabola ?

using h for y and t for x.
\[ h = -16t^2 + 64 t \]

do you know how to find the vertex of a parabola ? The vertex will be the highest part
This shows how to find the vertex
http://hotmath.com/hotmath_help/topics/vertex-of-a-parabola.html

Answer 2

find dh/dt - which equals the vertical velocity of the projectile - and set that to zero. then solve for t, which gives you the time at which the thing stops rising.

then plug that same t back into the original h(t) equation to find the max height.

Answer 3

thanks i really appreciate the help :)