At t sec after liftoff, the height of a rocket is \( 5 t^{2} \mathrm{ft} \). How fast is the rocket The speed of the rocket 9 seconds after liftoff is (Simplify your answer.)

To find the speed of the rocket at \( t = 9 \) seconds, we need to determine the derivative of the height function \( h(t) = 5t^2 \) with respect to time \( t \). The derivative, \( h'(t) \), gives us the velocity. Calculating the derivative: \[ h'(t) = \frac{d}{dt}(5t^2) = 10t \] Now, we can find the speed at \( t = 9 \) seconds: \[ h'(9) = 10 \times 9 = 90 \text{ ft/sec} \] So, the speed of the rocket 9 seconds after liftoff is \( 90 \text{ ft/sec} \).