Me and my friend are playing on a Ferris wheel which has Radius of 20 Meter and had an constant angular velocity of 0.2 rad/s .
Then, When I'm at the very top of the Ferris wheel i'm going to drop a tennis ball( dropping without initial velocity).
How far around the Ferris wheel in radian from me should my friend sit,
so he can catch the ball?
The acceleration of gravity is −9.8 m/s^2.
air resistance is neglected.
To determine the distance in radians from you that your friend should sit to catch the ball, we need to consider the time it takes for the ball to fall from the top of the Ferris wheel to your friend's position.
Here's how you can calculate it:
1. First, let's find the time it takes for the ball to fall from the top of the Ferris wheel to the bottom. We can use the equation of motion for vertical motion:
h = (1/2)gt^2,
where h is the height (equal to the radius of the Ferris wheel), g is the acceleration due to gravity (-9.8 m/s^2), and t is the time.
Plugging in the values:
20 = (1/2)(-9.8)t^2.
Solve this equation to find the time it takes for the ball to fall from the top to the bottom.
2. Once we know the time it takes for the ball to reach the bottom, we can calculate the angular displacement (in radians) your friend needs to be from you to catch the ball.
The angular displacement is given by the formula:
angular displacement = angular velocity * time.
Using the given angular velocity of 0.2 rad/s, and the time calculated from step 1, you can determine the angular displacement.
3. Finally, the distance in radians from you that your friend should sit is equal to the angular displacement calculated in step 2.
Note that the value obtained in step 3 is the angle in radians, and you can convert it to degrees if desired by using the conversion factor: 1 radian = 180/π degrees.
By following these steps, you should be able to determine how far around the Ferris wheel in radians your friend should sit to catch the ball.