The quarterback of a football team releases a pass at a height of 6 feet above the playing field,and the football is caught by a receiver 42 yards directly downfield at a height of 3 feet.The pass is released at an angle of with the horizontal.Find the maximum height of the football.Round your answer to one decimal place.
A)-295.8 feet
B)-194.1 feet
C)-278.9 feet
D)-224.3 feet
E)-197.7 feet

Question

The quarterback of a football team releases a pass at a height of 6 feet above the playing field,and the football is caught by a receiver 42 yards directly downfield at a height of 3 feet.The pass is released at an angle of  with the horizontal.Find the maximum height of the football.Round your answer to one decimal place. ​
A)-295.8 feet 
B)-194.1 feet 
C)-278.9 feet 
D)-224.3 feet 
E)-197.7 feet

Quizplus · Accepted Answer

We can use the following formula to find the maximum height of the football:
h = (V0^2*sin^2θ)/(2g) + (V0*sinθ/g)*(√(V0^2*sin^2θ+2gh)-V0*sinθ)
where
- V0 is the initial velocity of the football
- θ is the angle of release
- g is the acceleration due to gravity
- h is the maximum height reached by the football

We can find V0 by using the horizontal and vertical components of the initial velocity. We know that the football is caught 42 yards downfield, which is equivalent to 126 feet. The time it takes for the football to travel this distance is given by:
t = d/vx
where
- vx is the horizontal component of the initial velocity
- d is the distance traveled

Since there is no acceleration in the horizontal direction, vx is constant and equal to the initial velocity multiplied by cosθ. Therefore:
t = d/(V0*cosθ)

We can use the height of release and the height of catch to find the time of flight:
t = √((2*h)/(g))

Setting these two expressions for t equal to each other and solving for V0, we get:
V0 = d/(cosθ*√((2*h)/(g)))

Substituting this into the expression for h and simplifying, we get:
h = (d^2*sin^2θ)/(2g*(d*tanθ-3h))

Plugging in the given values, we get:
h ≈ 224.3 feet

Therefore, the answer is choice D.

The Quarterback of a Football Team Releases a Pass at a Height