Where to Place a Coin for a Ball to Strike Directly on Impact?

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

The coin should be placed 6 cm below the end of the ramp. How can we calculate this placement?

Calculation for Placing the Coin:

To find the location where the ball will strike the coin on impact with the ground, we can use the concept of time of flight. The time of flight is the time it takes for an object to travel from one point to another under the influence of gravity.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

The time of flight can be calculated using the following equation:

T = 2 * √(2*d / g)

Where:

T is the time of flight

d is the vertical distance the object falls

g is the acceleration due to gravity (approximately 9.8 m/s^2)

We know that the distance between the photogates is 30 cm and the time it takes for the ball to pass through is 0.20 s. Using this information, we can calculate the vertical distance the ball falls:

d = (1/2) * g * T^2

d = (1/2) * 9.8 * (0.20)^2

d = 0.98 m

Now, we can use this distance to calculate the vertical distance from the end of the ramp to where the coin should be placed:

Vertical distance from end of ramp to coin = 92 cm - 0.98 m

= 92 cm - 98 cm

= -6 cm

Therefore, the coin should be placed 6 cm below the end of the ramp.