Energy Loss & Height of Thrown Ball & Marble Fired from Cannon

AI Thread Summary
The discussion focuses on two physics problems involving energy loss and projectile motion. In the first problem, a 0.5 kg ball thrown upwards at 20 m/s reaches a maximum height of 15 m, prompting questions about energy loss due to air resistance and potential height without it. The second problem involves two children firing a marble from a spring-loaded cannon, with one child needing to adjust the spring compression to hit a target 2.40 m away after falling short. Participants suggest using energy equations to analyze the first problem and consider the effects of air resistance on height calculations. The conversation emphasizes understanding the principles of energy conservation and projectile motion in solving these scenarios.
Kuro
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1. A ball with a mass of 0.5 kg is thrown straight up with an initial speed of 20 m/s. The ball reaches a maximum height of 15 m. (a) Give the energy loss due to air resistance. (b) What height would the ball have reached without air resistance? (c) What height would the ball have reached on the moon (where gravity is only 0.17 that of earth)?

2. Two children are playing a game in which they try to hit a small box on the floor with a marble fired horizontally from a spring-loaded cannon that is mounted on a table. The target box is 2.40 m from the edge of the table. Alex compresses the spring 1.10 cm, but the marble falls 36 cm short. How far should Ben compress the spring to score a hit?
 
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How would you think to approach either of these problems?
 
In the first problem, I think that the energy loss is between the 1/2mv^2 - mgh?
 
Kuro said:
In the first problem, I think that the energy loss is between the 1/2mv^2 - mgh?

Not exactly, if you're looking for air resistance, though certainly that's the energy exchange in throwing a ball in the air.

Maybe consider how high it would go without any resistance using the relationship you suggested?
 
TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
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