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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

Respuesta :

we are given

[tex]f(d)=-0.6d^2+5.4d+0.8[/tex]

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

[tex]f(0)=-0.6(0)^2+5.4(0)+0.8[/tex]

[tex]f(0)=0.8[/tex]

So, initial height is 0.8 yard

Initial Velocity:

We can find derivative

[tex]f'(d)=-0.6\times 2d+5.4\times 1+0[/tex]

[tex]f'(d)=-1.2d+5.4+0[/tex]

now, we can plug d=0

[tex]f'(0)=-1.2(0)+5.4+0[/tex]

[tex]f'(0)=5.4[/tex]

so, initial velocity is 5.4 yard vertically / yard horizontally

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