Question

A ball is thrown upward in the air, and its height above the ground after t seconds is H ( t ) = 76 ⋅ t − 16 t 2 feet. Find the time t when the ball will be traveling upward at 19 feet per second.

Answer 1

5.34 m/s

Step-by-step explanation:

All the steps in the other answer are correct, find the derivative of H(t) and then set that answer equal to 19.

But for some reason my homework didn't like that answer. I found in my homework that you need times your answer by 3. I don't know why and multiplying by 3 worked for every problem except one. I was just gonna as this as a comment so if it doesn't work then feel free to give 1 star so I know that my reasoning is incorrect and I can take my answer down. I don't want to give people wrong answers for homework.

Answer 2

t = 1.78 s

Step-by-step explanation:

As we know that the height of the ball from ground is given as a function of time

`H = 76 t - 16 t^2`

now we know that rate of change in the position of ball is known as velocity of the ball

it is given as

`v = (dH)/(dt)`

`v = 76 - 32 t`

now we have to find the time at which the velocity of ball is 19 ft/s in upward direction so we have

`19 = 76 - 32 t`

`32 t = 76 - 19 = 57`

`t = 1.78 s`