Question

A student is standing on a very steep hill, kicks a soccer ball horizontally with a speed of 5 m/s toward a student who is sitting on a level field 2.3 meters below.

a. How long does it take the soccer ball to strike the ground?
b. If the second student catches the soccer ball at ground level, how far from the hill was she?
c. How fast was the soccer ball going when it hit the ground?"

Answer 1

The soccer ball's motion can be analyzed as a projectile motion problem to find the time to strike the ground, the horizontal distance traveled, and the final speed of the soccer ball upon impact.

Step-by-step explanation:

The situation described involves a player kicking a soccer ball from a steep hill to a person on a level field below, and the problem can be analyzed using the principles of projectile motion.

a. To calculate the time it takes for the soccer ball to strike the ground, we use the formula for the time of flight for vertical motion, which is solely dependent on the initial vertical velocity (which is zero since it is kicked horizontally) and the height. The formula derived from the equation of motion under gravity h = (1/2)gt² can be rearranged to solve for time t:

² = √(2h/g)

b. The distance the ball travels horizontally can be found by the horizontal velocity multiplied by the time it takes to hit the ground.

c. The final speed of the soccer ball when it hits the ground can be found by combining the horizontal velocity (which remains constant) and the vertical velocity at the time of impact. The vertical velocity can be found by the equation v = gt, where t is the time found in part (a). The final speed is then the vector sum of the horizontal and the vertical components.