The height of the ball increases until it reaches a

Tazmin Horton

Tazmin Horton

Answered question

2021-08-12

The height of the ball increases until it reaches a maximum height of 8 yards, 20 yards away from the player.
To find: Which kick travels further before hitting the ground.

Answer & Explanation

wheezym

wheezym

Skilled2021-08-13Added 103 answers

Step 1
Which kick travels higher.
Here the maximum height of the first ball is 8 yards.
When the ball reached its maximum height it was 20 yards away
from player, so the first ball travels 20(2)=40 yards
To find the maximum height find the value of vertex.
If the quadratic equation is of the form ax2+bx+c=0 then the vertex for the equation
ax2+bx+c=0 is x=b2a
Step 2
Given that a second kick is modelled by,
y=x(0.40.008x)
After solving,
y=0.4x0.008x2
Compare y=0.4x0.008x2 with ax2+bx+c get,
a=0.008, b=0.4, c=0.
So the vertex is,
x=ba
=0.40.008
=0.40.008
=25
x=25
Substitute x=25 in y=x(0.40.008x),
y=25(0.40.008(25))
y=25(0.40.2)
y=5
So the maximum height of the second ball is 5 yards and the second ball travels
25(2)=50 yards.
Step 3
Therefore,
The maximum height of the second ball is 5 yards and the second ball travels 25(2)=50 yards.

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