Question

The path of a football can be modelled by the equation, h=-10d2+120d , where h represents the height, in metres, of the football above the ground and d represents the horizontal distance, in metres, of the football from the player. At what horizontal distance does the football land?

Answer 1

Answer:

12 m

Step-by-step explanation:

The path of a football has been modeled by the equation:

$h= -10d^2+120d$

where h represents the height and d represents the horizontal distance.

When the ball lands, it means that its height is back at 0 metres. This means that we have to find horizontal distance, d, when height, h, is 0.

=> $0= -10d^2+120d$

$=> 10d^2 - 120d = 0$

$d(10d - 120) = 0$

∴ d = 0 m

and

10d - 120 = 0

=> d = 120 / 10 = 12 m

There are two solutions for d when h = 0 m.

The first solution (d = 0 m) is a case where the ball has not been thrown at all. This means the ball has not moved away from the football player and it is still on the ground.

The second solution is the answer to our problem (d = 12 m). The ball lands at a horizontal distance of 12 m