A rocket is launched, and its height above sea level t seconds after launch is given by the equation h(t)=−4.9t2+1000t+200

Question

A rocket is launched, and its height above sea level t seconds after launch is given by the equation h(t)=−4.9t2+1000t+200

a) From what height was the rocket launched?

b) What is the maximum height the rocket reaches?

c) If the rocket will splash down in the ocean, when will it splash down?

Answer 1

h'(t) = -9.8t +1000 = 0

time at max height = 1000/9.8 = about 102 seconds

max height = h(102) = -4.9(102)^2 +1000(102) + 200 = 102,200 - 50,980 = 51,220 meters

the rocket was launched from 200 meters high. the constant term in the quadratic polynomial is the initial height, t coefficient is the initial velocity. the squared term is the deceleration due to gravity.

splashdown time is found by setting h(t) = 0 and solving for t. It should be about 204+ seconds, a little over twice the time to reach max height

h(t) = -4.9t^2 +1000t + 200 = 0

use the quadratic formula

t = 102 + (1/9.8)sqr(1000^2 +4(4.9)(200)) = 102 + 102.2 = 204.2 seconds