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A child ties a stone to a rope and rotates the stone in a circumference in a 45-degree-to-vertical orientation at a constant speed. Relative to the ground, the lowest height of the stone is 0.5 of the highest height. For every half of the circle, the stone's average acceleration is 20 times the acceleration of gravity. Consider the dimensions of the stone negligible. (a) Determine an analytical equation (equality) that explicitly relates the acceleration of gravity (do not use a numerical value), the highest height and the square of the speed of the stone. (b) Once the rope snaps at the point where the centripetal acceleration is maximum, determine an analytical (equality) equation that explicitly relates the highest height and horizontal reach of the stone. (c) Determine the angle with respect to the horizontal of the velocity vector of the stone just before it hits the ground.

A child ties a stone to a rope and rotates the stone in a circumference in a 45-degree-to-vertical orientation at a constant speed. Relative to the ground, the lowest height of the stone is 0.5 of the highest height. For every half of the circle, the stone's average acceleration is 20 times the acceleration of gravity. Consider the dimensions of the stone negligible. (a) Determine an analytical equation (equality) that explicitly relates the acceleration of gravity (do not use a numerical value), the highest height and the square of the speed of the stone. (b) Once the rope snaps at the point where the centripetal acceleration is maximum, determine an analytical (equality) equation that explicitly relates the highest height and horizontal reach of the stone. (c) Determine the angle with respect to the horizontal of the velocity vector of the stone just before it hits the ground.

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A child ties a stone to a rope and rotates the stone in a circumference in a 45-degree-to-vertical orientation at a constant speed. Relative to the ground, the lowest height of the stone is 0.5 of the highest height. For every half of the circle, the stone's average acceleration is 20 times the acceleration of gravity. Consider the dimensions of the stone negligible. (a) Determine an analytical equation (equality) that explicitly relates the acceleration of gravity (do not use a numerical value), the highest height and the square of the speed of the stone. (b) Once the rope snaps at the point where the centripetal acceleration is maximum, determine an analytical (equality) equation that explicitly relates the highest height and horizontal reach of the stone. (c) Determine the angle with respect to the horizontal of the velocity vector of the stone just before it hits the ground.
Transcribed Image Text:A child ties a stone to a rope and rotates the stone in a circumference in a 45-degree-to-vertical orientation at a constant speed. Relative to the ground, the lowest height of the stone is 0.5 of the highest height. For every half of the circle, the stone's average acceleration is 20 times the acceleration of gravity. Consider the dimensions of the stone negligible. (a) Determine an analytical equation (equality) that explicitly relates the acceleration of gravity (do not use a numerical value), the highest height and the square of the speed of the stone. (b) Once the rope snaps at the point where the centripetal acceleration is maximum, determine an analytical (equality) equation that explicitly relates the highest height and horizontal reach of the stone. (c) Determine the angle with respect to the horizontal of the velocity vector of the stone just before it hits the ground.
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