A launched rocket has an altitude, in meters, given by the polynomial h+vt-4.9t^2, where h is the height, in meters, from which the launch occurs, at the velocity v in meters per second, and the t is the number of seconds for which the rocket is airborne. If a rocket is launched from the top of a tower 150 meters high with an initial upward speed of 60 meters per second, what will its height be after 4 seconds?

Question

A launched rocket has an altitude, in meters, given by the polynomial h+vt-4.9t^2, where h is the height, in meters, from which the launch occurs, at the velocity v in meters per second, and the t is the number of seconds for which the rocket is airborne. If a rocket is launched from the top of a tower 150 meters high with an initial upward speed of 60 meters per second, what will its height be after 4 seconds?

Answer 1

h=150m

v=60m/s
t=4s
height of rocket=h+vt-4.9t^2
=150+(60x4)-4.9x4^2
=311.6m

Answer 2

To find the rocket's height after 4 seconds, we need to substitute the values into the given polynomial.

Given:
h = 150 meters (height from which the launch occurs)
v = 60 meters per second (initial upward velocity)
t = 4 seconds (time elapsed)

Substituting these values into the polynomial h + vt - 4.9t^2:

Height = h + vt - 4.9t^2
= 150 + (60 * 4) - 4.9 * (4^2)
= 150 + 240 - 4.9 * 16
= 150 + 240 - 78.4
= 390 - 78.4
= 311.6 meters

Therefore, the rocket's height after 4 seconds will be 311.6 meters.