A football was thrown from the line of scrimmage with a velocity of

30 m/s at an angle of 30o above the horizontal.

(a) Determine the time required by the ball to reach the maximum height of its flight path.

(b)Determine the distance from the line of scrimmage that a receiver must travel in order to catch the ball just before it hits the ground.

Vo = 30m/s @ 30 Deg

Vo = 30m/s @ 30 Deg.
xo = hor = 30*cos30 = 26 m/s.
Yo = ver = 30*sin30 = 15 m/s.

a. Tr = (Y-Yo)/g.
Tr = (0-15) / 9.8 = 1.53 s. = Rise time
or time to reach max. ht.

b. D = Vo^2*sin(2A)/g.
D = 900*sin60 / 9.8 = 79.5 m.

post it.

To answer these questions, we can use the kinematic equations of motion to analyze the projectile motion of the football.

(a) To determine the time required by the ball to reach the maximum height of its flight path, we can use the equation for vertical displacement:

Δy = Vyi * t - (1/2) * g * t^2

In this equation:
- Δy is the change in vertical position (in this case, the maximum height above the ground)
- Vyi is the vertical component of the initial velocity (in this case, Vyi = V * sin(θ))
- t is the time taken to reach the maximum height
- g is the acceleration due to gravity (approximately 9.8 m/s^2)

Since the ball reaches its maximum height at the instant its vertical velocity becomes zero, we can set Vyi * t - (1/2) * g * t^2 = 0 and solve for t.

Vyi * t - (1/2) * g * t^2 = 0

V * sin(θ) * t - (1/2) * g * t^2 = 0

Simplifying and rearranging the equation, we get:

(1/2) * g * t^2 = V * sin(θ) * t

Dividing both sides by t (assuming t is not equal to zero), we get:

(1/2) * g * t = V * sin(θ)

Solving for t, we finally get:

t = (2 * V * sin(θ)) / g

Plugging in the given values (V = 30 m/s, θ = 30o, g = 9.8 m/s^2):

t = (2 * 30 * sin(30)) / 9.8

Now, we can calculate the value of t to determine the time required by the ball to reach the maximum height.

(b) To determine the distance from the line of scrimmage that a receiver must travel to catch the ball just before it hits the ground, we can use the equation for horizontal displacement:

Δx = Vxi * t

In this equation:
- Δx is the horizontal displacement (distance from the line of scrimmage)
- Vxi is the horizontal component of the initial velocity (in this case, Vxi = V * cos(θ))
- t is the time of flight (twice the time required to reach the maximum height, as the total flight time is symmetrical for a projectile)

Plugging in the given values (V = 30 m/s, θ = 30o) and using the value of t calculated in part (a), we can calculate the horizontal displacement to determine the distance from the line of scrimmage.

Δx = V * cos(θ) * t

Now, you can calculate the values of t and Δx using the equations explained above to find the answers to both parts of the question.