A player kicks the football from the ground with a velocity of of 30m/s at 45 degree angle. Find the initial vertical velocity?

To find the initial vertical velocity of the football, we need to decompose the given velocity into its horizontal and vertical components.

The given velocity is 30 m/s at an angle of 45 degrees.

First, we need to find the horizontal component of the velocity.

The horizontal component of the velocity, denoted as Vx, can be found using the formula:

Vx = V * cos(theta)

Where V is the magnitude of the velocity (30 m/s) and theta is the angle (45 degrees).

Substituting the values into the formula:
Vx = 30 * cos(45)

To evaluate cos(45), we can use the trigonometric identity: cos(45) = sqrt(2) / 2.

Vx = 30 * (sqrt(2) / 2) = 30 * sqrt(2) / 2 = 15 * sqrt(2) m/s

Now, we can find the initial vertical velocity, denoted as Vy.

The vertical component of the velocity can be found using the formula:

Vy = V * sin(theta)

Substituting the values into the formula:
Vy = 30 * sin(45)

To evaluate sin(45), we can use the trigonometric identity: sin(45) = sqrt(2) / 2.

Vy = 30 * (sqrt(2) / 2) = 30 * sqrt(2) / 2 = 15 * sqrt(2) m/s

Therefore, the initial vertical velocity of the football is 15 * sqrt(2) m/s.

To find the initial vertical velocity of the football, we need to first break down the initial velocity into its horizontal and vertical components.

Given:
Initial velocity (v) = 30 m/s
Launch angle (θ) = 45 degrees

The vertical component of the initial velocity (v_y) can be found using the equation:

v_y = v * sin(θ)

Substituting the given values:

v_y = 30 * sin(45)

Using a scientific calculator, we can calculate:

v_y ≈ 21.21 m/s

Therefore, the initial vertical velocity of the football is approximately 21.21 m/s.