Final answer:
Using the initial horizontal and vertical velocities and kinematic equations, we can solve for the speed at impact, the time the ball is airborne, and the maximum height it reaches in the context of projectile motion in physics.
Step-by-step explanation:
The question involves calculating the speed of a soccer ball when it hits the ground, the duration the ball remains in the air, and the maximum height it reaches, using principles of projectile motion in physics. To determine these factors, we use the given initial velocities in both the horizontal and vertical directions, the gravity's influence on the ball's vertical motion, and kinematic equations.
Calculating the Speed When the Ball Hits the Ground
We consider the initial vertical and horizontal velocities and use Pythagoras' theorem because the horizontal velocity remains constant and the final vertical velocity can be found using kinematic equations.
Time of Flight
To find the duration the ball is in the air, we only consider the vertical motion because gravity only affects the vertical component of velocity. We use the equation for vertical motion and solve for time when the vertical displacement is zero (the time it takes for the ball to go up and come back down).
Maximum Height
The maximum height is reached when the vertical velocity is zero. We use the vertical component of the initial velocity and the acceleration due to gravity to find out the time it takes to reach this point and then calculate the height.