A quarterback throws the football to a sta-

tionary receiver who is 26 m down the field.
The football is thrown at an initial angle of
36.5� to the ground.
The acceleration of gravity is 9.81 m/s2 .
a) At what initial speed must the quarter-
back throw the ball for it to reach the receiver?
Answer in units of m/s

range = 26 m = (Vo^2/g)*sin(2*36.5)

26 = (Vo^2/9.81)*sin73

Vo^2 = 266.7 m^2/s^2
Vo = ?

To find the initial speed at which the quarterback must throw the ball, we can use the equations of projectile motion. When the quarterback throws the ball, it follows a parabolic trajectory due to the combination of initial velocity and gravity.

Let's break down the problem into its components:
- The horizontal component: The ball moves only horizontally, with a constant velocity. There is no acceleration in this direction.
- The vertical component: The ball moves vertically, under the influence of gravity. We need to find the initial speed in this direction.

Since we know the initial angle and the acceleration due to gravity, we can use the equations of motion to find the initial speed of the ball in the vertical direction.

Step 1: Determine the vertical and horizontal components of the initial velocity.
The vertical component of the initial velocity can be found using the following equation:
Vy = V₀sinθ

Where Vy is the vertical component of the initial velocity, V₀ is the initial speed, and θ is the initial angle of 36.5 degrees.

Step 2: Find the time of flight of the ball.
The time it takes for the ball to reach the receiver can be found using the following equation:
t = (2Vy) / g

Where g is the acceleration due to gravity (9.81 m/s²).

Step 3: Use the time of flight to find the horizontal distance.
The horizontal distance traveled by the ball can be calculated using this equation:
D = Vx * t

Where D is the horizontal distance traveled, Vx is the horizontal component of the initial velocity (which remains constant throughout the trajectory), and t is the time of flight calculated in Step 2.

Step 4: Determine the initial speed.
Using the horizontal distance and the known value of 26 meters, we can set up the following equation:
D = V₀cosθ * t

We can rearrange this equation to solve for V₀:
V₀ = D / (cosθ * t)

Now we can substitute the values we know into the equation and calculate the answer.

V₀ = 26 / (cos(36.5°) * (2*(sin(36.5°)) / 9.81))

Using a scientific calculator or a math software, we can evaluate this expression to find the initial speed V₀.