Understanding the Physics

* Projectile Motion: The football's trajectory is a classic example of projectile motion, where the only force acting on it is gravity after the initial kick.

* Horizontal and Vertical Components: We need to consider the horizontal (x) and vertical (y) components of the football's velocity.

* Time of Flight: The time the ball spends in the air is related to its vertical velocity.

* Range: The horizontal distance traveled (50 m) is related to the horizontal velocity and the time of flight.

Solution

1. Vertical Motion:

* We know the time of flight (t) is 3 seconds.

* The acceleration due to gravity (g) is -9.8 m/s².

* Using the equation:

* t = 2 * (v_y / g) (where v_y is the initial vertical velocity)

* We can solve for v_y:

* v_y = (g * t) / 2 = (-9.8 m/s² * 3 s) / 2 = -14.7 m/s

* The negative sign indicates the initial vertical velocity is upwards.

2. Horizontal Motion:

* The horizontal velocity (v_x) remains constant throughout the flight.

* We can use the range (R) and time (t) to find v_x:

* R = v_x * t

* v_x = R / t = 50 m / 3 s = 16.67 m/s

3. Angle of Kick (θ):

* The angle of the kick (θ) is related to the horizontal and vertical components of velocity:

* tan(θ) = v_y / v_x

* θ = arctan(v_y / v_x) = arctan(-14.7 m/s / 16.67 m/s) ≈ -41.8°

Important Note: The angle is negative because the initial vertical velocity is upwards. To express the angle relative to the horizontal, we take the absolute value:

Therefore, the angle of the kick is approximately 41.8° above the horizontal.