How to Calculate the Horizontal Distance a Ball Travels While Falling from a Ramp

What is the process of finding where a coin should be placed so that a ball strikes it directly on impact with the ground?

Where should a coin be placed so that the ball strikes it directly on impact with the ground?

Calculation Process:

To determine where the coin should be placed so that the ball strikes it directly on impact with the ground, we need to find the horizontal distance the ball travels while falling from the end of the ramp to the ground.

In order to calculate the horizontal distance a ball travels while falling from a ramp to the ground, we can use the equations for horizontal and vertical motion. The horizontal distance (dx) can be determined by using the equation:

dx = vt

Where dx is the horizontal distance, v is the horizontal velocity of the ball, and t is the time it takes for the ball to fall.

Additionally, the vertical distance (dy) the ball travels can be calculated using the equation:

dy = 0.5gt^2

Where dy is the vertical distance, g is the acceleration due to gravity, and t is the time it takes for the ball to fall. By substituting the given values and solving the equations, we can find the horizontal distance (dx) and place the coin at that distance from the ramp's end, considering the direction of the ball's motion.