Answer :
Final answer:
The magnitude of the centripetal acceleration of the stone while in circular motion is approximately 1.30 x 10^6 m/s². This was determined by first calculating the time of flight using the height and acceleration due to gravity, then using this to figure out the velocity, and finally using the velocity and radius to calculate the centripetal acceleration.
Explanation:
The question is asking for the centripetal acceleration of the stone while it's in circular motion. To find this, we need to start by noting that when the stone flies off horizontally, it still experiences the acceleration due to gravity (g) as it falls. The time (t) it takes for the stone to hit the ground can be found using the formula h = 0.5gt², where h is the height above ground. Substituting the given values gives t = √(2h/g) = √((2*2.10 m) / 9.81 m/s²) ≈ 0.654 s.
Next, we use the time t to find the velocity (v) of the stone as it flies off, using the formula v = d/t, where d is the horizontal distance. This gives us v = 970 m / 0.654 s ≈ 1483 m/s.
Finally, we plug the values of v and the radius (r) into the formula for centripetal acceleration, a = v²/r. This gives us a = (1483 m/s)² / 1.69 m ≈ 1.30 × 10^6 m/s².
So the magnitude of the centripetal acceleration of the stone while in circular motion is approximately 1.30 × 10^6 m/s².
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