Question

when the ball is dropped from a higher point, it makes a deeper indent in the sand. what does this suggest about its energy? it had less potential energy at the higher height it had more potential energy and transferred more energy to the sand the sand was softer at higher heights the ball was lighter at higher heights

Explanation:

• Potential energy formula: \(U = mgh\) (where \(m\) is mass, \(g\) is acceleration due to gravity, \(h\) is height). When \(h\) (height) increases (ball is dropped from a higher point), potential energy \(U\) increases (assuming \(m\) and \(g\) are constant).
• The deeper indent in the sand means more work is done on the sand. Work done is related to energy transfer. More potential energy at the higher - height is converted to more kinetic energy just before hitting the sand, and then more energy is transferred to the sand (as work done to make the indent).
• Option 1: Incorrect. As \(h\) increases (higher point), potential energy \(U=mgh\) increases (not less).
• Option 3: Incorrect. The property of the sand (softness) is not related to the height from which the ball is dropped in this context.
• Option 4: Incorrect. The mass of the ball (related to weight \(W = mg\)) does not change with height (in a near - Earth situation where \(g\) is approximately constant).

Answer:

It had more potential energy and transferred more energy to the sand.