Question

A ball is kicked with an initial velocity of 16 m/s in the horizontal direction and 12 m/s in the vertical direction. (a) At what speed does the ball hit the ground? (b) For how long does the ball remain in the air? (c)What maximum height is attained by the ball?

At what speed does the ball hit the ground?
a) 20 m/s
b) 16 m/s
c) 12 m/s
d) 4 m/s

Answer 1

The ball hits the ground with a speed of 16 m/s, remains in the air for 0.8 seconds, and attains a maximum height of approximately 7.45 meters.

Step-by-step explanation:

To find the speed at which the ball hits the ground, we can consider the horizontal and vertical components of its velocity separately. The horizontal velocity remains unchanged throughout the motion, so the ball will hit the ground with a speed of 16 m/s (option c).

To find the time the ball remains in the air, we can use the equation d = v*t, where d is the vertical displacement and v is the initial vertical velocity. Since the ball starts and ends at the same vertical position, the displacement is 0, and thus, the time in the air is 0.8 seconds (option b).

The maximum height attained by the ball can be found using the equation v^2 = u^2 + 2as, where v is the final vertical velocity, u is the initial vertical velocity, a is the acceleration due to gravity (-9.8 m/s^2), and s is the displacement. Solving for s, we find that the maximum height is approximately 7.45 meters (option b).