Question

a rocket is fired upward from the ground with an initial velocity of 280 feet per second. neglecting air resistance, the height of the rocket at any time t can be described in feet by the polynomial $-16t^2 + 280t$. find the height of the rocket at $t = 7.5$ seconds. (simplify your answer.)

Explanation:

Step1: Substitute t = 7.5 into the polynomial

We have the height polynomial \( h(t)= -16t^{2}+280t \). Substitute \( t = 7.5 \) into it:
\( h(7.5)=-16\times(7.5)^{2}+280\times7.5 \)

Step2: Calculate \( (7.5)^{2} \)

First, calculate \( (7.5)^{2}=7.5\times7.5 = 56.25 \)

Step3: Calculate the first term

Then, calculate \( -16\times56.25=-900 \)

Step4: Calculate the second term

Next, calculate \( 280\times7.5 = 2100 \)

Step5: Sum the two terms

Now, sum the two results: \( -900 + 2100=1200 \)

Answer:

1200