Question

A model rocket is launched directly upward at a speed of 16 meters per second from a height of 2 meters. The function f(t)=−4.9t2+16t+2, models the relationship between the height of the rocket and the time after launch, t, in seconds. Which is the maximum height, in meters, the rocket will reach?

Answer 1

`Hmax=15.06` meters

Explanation:The question ask for the maximum value of the function f(t) which can be find by find the maxima of the function

The maxima of the function occurs when the slope is zero. i.e.

`(df)/(dt) =0\\(df)/(dt) =(d)/(dt) (-4.9t^2+16t+2)\\(df)/(dt) =-4.9*2t+16\\-9.8t+16=0\\t=16/9.8\\t=1.63 secs`

Hence the maxima occurs at t=1.63 seconds

The maximum value of f is

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

hence maximum height is found to be

`Hmax=15.06` meters