a rocket is fired upward from a planet (not earth). The height in meters after t seconds is given by the function h(t)=-2.3t^2+41t.

Question

1. when will the rocket reach a height of 160 meters?

2.when will it attain it's maximum height and what is its maximum height ?

3. when will the rocket return to the ground ?

Answer 1

1. The rocket will reach a height of 160 meters when h(t)=160.

    Let -2.3t^2+41t=160

    2.3t^2-41t+160=0

    Using the quadratic formula, t = 5.77 and 12.06 seconds.

 

2. The rocket will reach its maximum height when h'(t)=0.

    h'(t)=-4.6t+41

    Let -4.6t+41=0

    So t=41/4.6=8.9 seconds.

    Its maximum height is the height at 8.9 seconds, which is h(8.9).

    h(8.9)=-2.3(8.9)^2+41(8.9)=182.72 meters.

 

3. The rocket will return to the ground when the height is 0 meters, which means that h(t)=0.

    Let h(t)=-2.3t^2+41t=0

    Solving for t, t=0 or 41/2.3. Since t=0 is when you are firing the rocket, the rocket returns in 41/2.3, or 17.83 seconds.