A football is thrown upward at a(n) 37� angle

to the horizontal.
The acceleration of gravity is 9.8 m/s2 .
To throw a(n) 57.8 m pass, what must be
the initial speed of the ball?
Answer in units of m/s

Think on this. to go L meters horizontally, it has to be in the air T seconds.

in the horizontal
L=vi*cosTheta*t-1/2 g t^2 where you solve for t in terms of the other unknowns (such as vi).

now in the vertical, the final position is the same as the initial position
vf=vi*sinTheta - g t
0=vi*sinTheta-g t put in the expression you found for t above, and solve for vi.

To find the initial speed of the ball, we can make use of the basic principles of projectile motion.

First, let's break down the given information:
- The football is thrown upward at an angle of 37 degrees to the horizontal.
- The acceleration of gravity is 9.8 m/s^2.
- We want to determine the initial speed of the ball to cover a pass distance of 57.8 m.

Now, let's analyze the motion of the ball:
1. Horizontal Motion:
Since the initial speed is the only component responsible for the horizontal motion, it remains constant throughout the motion. The horizontal distance covered by the ball is given as 57.8 m.

2. Vertical Motion:
The vertical motion of the ball can be split into two parts: upward motion and downward motion. At the highest point of the trajectory, the ball's vertical velocity becomes zero.

Now, we can use the kinematic equations to solve for the initial speed:
1. Vertical Motion Equation:
When the ball reaches its highest point, the vertical component of its velocity will be zero:
Vf = Vi + at
0 = Vi - gt

2. Total Time of Flight:
The total time of flight can be calculated using the formula:
t = 2 * (Vertical component of velocity / g)

3. Horizontal Motion Equation:
Since we have the horizontal distance and time, we can calculate the horizontal component of velocity using the formula:
Horizontal distance = Horizontal component of velocity * time

Putting it all together, we can solve for the initial speed of the ball:
1. Solve for the vertical component of the initial velocity:
Vi = gt

2. Calculate the time of flight:
t = 2 * (Vi / g)

3. Find the horizontal component of the velocity:
Horizontal component of velocity = Horizontal distance / time

4. Calculate the initial speed of the ball using the Pythagorean theorem:
Initial speed = sqrt((Horizontal component of velocity)^2 + (Vertical component of velocity)^2)

Plugging in the values and evaluating the equations, we can find the initial speed of the ball.