Answer:
The distance travelled by ball is 98 units before it again reaches the same height from which it was thrown.
Step-by-step explanation:
The given parabolic equation is
[tex]y=-\frac{3}{2401}(x-49)^2+8.5[/tex]
Where, h is height of ball after covering x distance horizontally.
Put x=0, to find initial height of the ball.
[tex]y=-\frac{3}{2401}(0-49)^2+8.5[/tex]
[tex]y=-3+8.5[/tex]
[tex]y=5.5[/tex]
Put y=5.5 in the given equation and find the values of x at which the height of ball is 5.5.
[tex]5.5=-\frac{3}{2401}(x-49)^2+8.5[/tex]
[tex]\frac{3}{2401}(x-49)^2=-5.5+8.5[/tex]
[tex]\frac{3}{2401}(x-49)^2=3[/tex]
[tex](x-49)^2=2401[/tex]
Take square root both sides.
[tex]x-49=\pm 49[/tex]
[tex]x=\pm 49+49[/tex]
[tex]x=0,98[/tex]
The height of ball is 5.5 at x=0 and x=98.
Therefore distance travelled by ball is 98 units before it again reaches the same height from which it was thrown.
