Question

question 25
the height, ( h(t) ), in feet of a football thrown from a skyscraper after ( t ) seconds is given by ( h(t) = -16t^2 + 73.3t + 325 ).
find the velocity of the football after 7 seconds.
150.7 feet per second
-54.1 feet per second
54.1 feet per second
-150.7 feet per second

Explanation:

Step1: Differentiate height for velocity

The velocity function $v(t)$ is the derivative of the height function $h(t)$. Using power rule: $\frac{d}{dt}(t^n)=nt^{n-1}$
$v(t) = h'(t) = \frac{d}{dt}(-16t^2 + 73.3t + 325) = -32t + 73.3$

Step2: Substitute $t=7$ into $v(t)$

Calculate velocity at 7 seconds.
$v(7) = -32(7) + 73.3$

Step3: Compute the final value

Simplify the arithmetic expression.
$v(7) = -224 + 73.3 = -150.7$

Answer:

-150.7 feet per second