Question

Supposed the path of a baseball follows the past graphed by the quadratic function f(d)= -0.6d^2+5.4d+0.8 where d is the horizontal distance the ball traveled in yards, and f(d) is the height, in yards of the ball at d horizontal yards. Find the initial height and the initial velocity of the ball.

A. Initial height: 5.4 yards, initial velocity: 0.8 yards vertically/yard horizontally

B. Initial height: 0.8 yards, initial velocity: 5.4 yards vertically/yard horizontally

C. Initial height: 0.8 yards, initial velocity: 0.6 yards vertically/yard horizontally

D. Initial height: 0.6 yards, initial velocity: -5.4 yards vertically/yard horizontally

Answer 1

we are given

`f(d)=-0.6d^2+5.4d+0.8`

where

d is the horizontal distance the ball traveled in yards

f(d) is the height, in yards of the ball at d horizontal yards

Initial height:

For finding initial height , we can plug d=0

`f(0)=-0.6(0)^2+5.4(0)+0.8`

`f(0)=0.8`

So, initial height is 0.8 yard

Initial Velocity:

We can find derivative

`f'(d)=-0.6* 2d+5.4* 1+0`

`f'(d)=-1.2d+5.4+0`

now, we can plug d=0

`f'(0)=-1.2(0)+5.4+0`

`f'(0)=5.4`

so, initial velocity is 5.4 yard vertically / yard horizontally

Hence , option-B.......Answer