The motion of the ball is a composition of two motions:
- on the x (horizontal) axis, it is a uniform motion with initial velocity
- on the y (vertical) axis, it is a uniformly accelerated motion with acceleration
(a) to solve this part, we just analyze the motion on the vertical axis. The law of motion here is
By requiring y(t)=0, we find the time t at which the ball reaches the floor:
(b) for this part, we can analyze only the motion on the horizontal axis. To find how far the ball will land, we must calculate the distance covered on the x-axis, x(t), when the ball reaches the ground (so, after a time t=0.64 s):
- on the x (horizontal) axis, it is a uniform motion with initial velocity
- on the y (vertical) axis, it is a uniformly accelerated motion with acceleration
(a) to solve this part, we just analyze the motion on the vertical axis. The law of motion here is
By requiring y(t)=0, we find the time t at which the ball reaches the floor:
(b) for this part, we can analyze only the motion on the horizontal axis. To find how far the ball will land, we must calculate the distance covered on the x-axis, x(t), when the ball reaches the ground (so, after a time t=0.64 s):