Question

A toy rocket is shot upward into the air from an initial 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)=1/2at^2+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 maximum height. How high above the ground is the toy rocket when it explodes? ​

Answer 1

20.1 m.

Explanation:

To find the maximum height we convert to vertex form:

h = 1/2 * -9.8 t^2 + 19.6t + 0.5

h = -4.9t^2 + 19.6t + 0,5

h = -4.9(t^2 - 4t) + 0.5

h = -4.9 [ (t - 2)^2 - 4] + 0.5

h = -4.9(t - 2)^2 + 19.6 + 0.5

y = -4.9(t - 2)^2 + 20.1

So the answer is 20.1 metres.