Question

A model rocket launched directly upward at a speed of 16 meters per second from a helght of 2 meters . The f(t) = - 4.9t ^ 2 + 16t + 2 models the relationship between the height of the rocket and the time after launch, t. In seconds. Which is the maximum height meters the rocket will reach Round to two decimal places Provide your answer below: meters

Answer 1

f(t) = 15.06 m

Explanation:

The relationship between the height of the rocket and the time after launch, t. In seconds is given by :

`f(t) = - 4.9t ^ 2 + 16t + 2`

We need to find the maximum height the rocket will reach the ground.

When it reaches the ground,

f(t) = 0

So,

Maximum height,

f'(t) = 0

`-9.8t+16=0\\\\t=(16)/(9.8)\\\\t=1.63\ s`

Put t = 1.63 in equation (1).

`f(1.63) = - 4.9* (1.63 ^ 2) + 16(1.63) + 2\\\\=15.06\ m`

So, the maximum height of the rocket is 15.06 m.