A ball rolls off a shelf with a horizontal velocity of v. At what horizontal distance from the shelf does the ball land if the height of the shelf is h above the floor?
find how long it takes to fall h meters.
Knowing the falling time t, in seconds,
horizontal distance= horizontal velocity*t
To find the horizontal distance at which the ball lands, we can use the equations of motion and consider the horizontal motion of the ball, assuming no air resistance.
Firstly, we need to determine the time it takes for the ball to hit the ground. The vertical motion of the ball can be described by the equation:
h = (1/2) * g * t^2
where h is the height of the shelf above the floor, g is the acceleration due to gravity (approximately 9.8 m/s^2), and t is the time taken to reach the ground.
Simplifying the equation, we can express t in terms of h:
t = sqrt((2 * h) / g)
Now, since the horizontal velocity of the ball doesn't change, the distance traveled in the horizontal direction (d) is given by:
d = v * t
Substituting the value of t from the previous equation:
d = v * sqrt((2 * h) / g)
Therefore, the horizontal distance from the shelf where the ball lands is equal to v times the square root of (2 times the height of the shelf divided by the acceleration due to gravity).