Question

a rocket is fired upward from the ground with an initial velocity of 220 feet per second. neglecting air resistance, the height of the rocket at any time t can be described in feet by the polynomial (-16t^2 + 220t). find the height of the rocket at (t = 6) seconds. (simplify your answer.) time, t (in seconds): 6; height: (-16t^2 + 220t)

Explanation:

Step1: Substitute t = 6 into the polynomial

We have the height polynomial \( h(t)= -16t^{2}+220t \). Substitute \( t = 6 \) into it:
\( h(6)=-16\times(6)^{2}+220\times6 \)

Step2: Calculate the square and multiplications

First, calculate \( (6)^{2}=36 \). Then:
\( -16\times36=-576 \)
\( 220\times6 = 1320 \)

Step3: Add the two results

Now, add \( -576 \) and \( 1320 \):
\( -576 + 1320=744 \)

Answer:

744