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Assume that Quick Release lets go of the ball 6 feet above the ground and the receiver
catches it 6 feet above the ground. The ball reaches a maximum height of 16 feet above
the ground halfway to the receiver. Write an algebraic rule that models the path of the
football. Show all your work and explain your reasoning.

Respuesta :

onyebuchinnaji

The equation that models the path of the football released from the given position is h(t) = -10 + 25.37t - 16.1t².

Initial velocity of the ball

The initial velocity of the ball is determined by applying third kinematic equation as shown below;

Vf² = V₀² - 2gh

  • at maximum height, the final velocity, Vf = 0
  • maximum height reached from the point of projection, = 16 ft - 6ft = 10 ft

0 = V₀² - 2gh

V₀² = 2gh

V₀ = √(2gh)

V₀ = √(2 x 32.17 x 10)

V₀ = 25.37 ft/s

Equation of motion of the ball

The equation of the ball's motion can be modelled as follows;

h = V₀t - ¹/₂gt²

10 = 25.37t - ¹/₂(32.17)t²

10 = 25.37t - 16.1t²

h(t) = -10 + 25.37t - 16.1t²

Thus, the equation that models the path of the football at any given position is h(t) = -10 + 25.37t - 16.1t².

Learn more about equation of motion here: https://brainly.com/question/25951773

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