Question

Speed of a rocket At t sec after liftof, the height of a rocket is 3t 2 ft. How fast is the rocket climbing 10 sec after liftof?

Answer 1

The speed of the rocket 10 seconds after liftoff is 60 ft/s.

Step-by-step explanation:

To find the speed of the rocket 10 seconds after liftoff, we can differentiate the equation for the height of the rocket with respect to time. In this case, the equation for the height of the rocket is given as h = 3t^2. Taking the derivative of this equation with respect to time will give us the rate of change of height with respect to time, which is the speed of the rocket. The derivative of 3t^2 with respect to t is 6t. Plugging in t = 10 into the derivative, we get 6(10) = 60.

Answer 2

Physically the derivative of the position of an object is equivalent to the function that describes its velocity. Therefore we will derive the function and then evaluate it within 10 seconds.

Our function is initially given as

`f(x) = 3t^2`

`f'(x) = 6t`

Evaluating at 10 seconds we have,

`f'(x) = 6(10)`

`f'(x) = 60`

Therefore the rocket climb to 60m/s