What is the Required Centripetal Acceleration for a Stone to Reach 25 Meters?

[gonzalo12345]

Homework Statement

You plan to throw stones by using a sling of length 1.3 m which you whirl over your head. Suppose you wish to throw a stone a distance of 25 m. What must be the centripetal acceleration of the stone just before its release if it is to reach this distance? Assume that the release height is 2.7 m.

Homework Equations

ac = v^2/r = (w^2)r = (4((pi)^2)r)/(T^2)

The Attempt at a Solution

I really don't know how to start this problem

 

[Doc Al]

First figure out how fast you have to throw the stone to reach that distance. Hint: Assuming the stone is released horizontally, how long is it in the air?

 

[baba89]

as it is missing some crucial information. In order to calculate the centripetal acceleration, we need to know the velocity of the stone and the radius of the circular motion. We also need to know the time it takes for the stone to travel 25 m in order to calculate the angular velocity (w). Without these values, it is impossible to accurately determine the centripetal acceleration.

However, we can make some assumptions and estimations to provide a rough estimate of the centripetal acceleration. Let's assume that the stone is thrown with an initial velocity of 10 m/s and the radius of the circular motion is 1.3 m (equal to the length of the sling). We can then calculate the angular velocity using the equation w = v/r = 10/1.3 = 7.69 rad/s.

Next, we can use the equation ac = (w^2)r to calculate the centripetal acceleration. Plugging in our estimated values, we get ac = (7.69^2)(1.3) = 75.7 m/s^2.

However, this is just a rough estimate and the actual centripetal acceleration could be different depending on the actual values of velocity, radius, and time. It is important to have all the necessary information in order to accurately solve a problem involving centripetal acceleration.