Question

A hockey player strikes a hockey puck. The height of the puck increases until it reaches a maximum height of 1.5 feet, 30 feet away from the player. The height y (in feet) of a second hockey puck is modeled by y=x(0.08−0.002x), where x is the horizontal distance (in feet). Compare the distances traveled by the hockey pucks before hitting the ground.

Answer 1

x₁ > x₂

Explanation:

Both actions imply a parable trajectories, since both are projectile shot cases.

Let´s call x₁ maximum distance in the first case

The maximum height is just in the middle of the curve, therefore x₁ the maximum horizontal distance is equal to 60 feet.

In the second case, the parable curve is modeled by:

y = x₂*( 0.08 - 0.002x₂) or y = 0.08*x₂ - 0.002*x₂²

A second degree equation, solving for x₂ and dismissing the value x₂ = 0

we get:

y = 0 ⇒ x₂*( 0.08 - 0.002x₂) = 0 x₂ = 0

And 0,08 - 0.002*x₂ = 0

- 0.002*x₂ = - 0.08

x₂ = 0.08/0.002

x₂ = 40 f

Then x₁ > x₂