Question

A toy rocket is shot upward into the air from a height of 1/2 meter above the ground with an initial velocity of 19.6 meters per second. The formula for the vertical motion of an object is h(t) = 1/2at² + vt + s. where the gravitational constant.a. is -9.8 meters per second squared, v is the initial velocity, s is the initial height, and h (t)is the height in meters modeled as a function of time, t.

Due to a malfunction, the toy rocket explodes when it reaches its maximum height. How high abov the ground is the toy rocket when it explodes? Round to the nearest tenth.

Answer 1

well all you really need to solve is the vertical problem
h(t) = 1/2at² + vt + s
v(t) = Vinitialup - g t = 0 at top
0 = 19.6 - 9.8 t
t = 2 seconds flying upward
then
h = (1/2) (-9.8) *4 + 19.6 * 2 + 0.5 *note it started 1/2 meter up
= -19.6 +39.2 + .5
= 20.1