Time in Air for Ball Rolling Down a Ramp

AI Thread Summary
The discussion revolves around calculating the time a ball is in the air after rolling down a ramp. The ball takes 0.750 seconds to travel 0.700 meters down the ramp and hits a mark 1.70 meters from the ramp's base. Two approaches to find the initial velocity are suggested: calculating average velocity based on ramp length and time, or using energy conservation principles (potential energy equals kinetic energy). The uniform acceleration of the ball is emphasized, indicating that the velocity upon leaving the ramp is double the average velocity. Understanding the ramp's angle is crucial for resolving the velocity in the x-direction and determining the time in the air.
bwagner
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Homework Statement



A ball is placed 0.700m from the end of a declining ramp and rolls down the ramp in 0.750s. The marble is also 0.175m from the horizontal. The ball hits a mark on the floor that is 1.70m from the bottom of the ramp on the x-axis. What mount of time is the ball in the air after leaving the ramp?

Homework Equations





The Attempt at a Solution


Can't find initial velocity.
 
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Seems like a couple of approaches are available: one is to simply find the average velocity from the length of the ramp anf the time spent. Since acceleration is uniform the velocity as it leaves the ramp is twice that (initial velocity is zero).

The other is to equate potantial energy loss with kinetic energy gain while on the ramp.

In other words, mgh=1/2mv^2

From there you need to know the angle of the ramp. Then resolve the velocity in the x direction. This help?
 
The velocity,as it leaves the ramp, is twice what? The calculated velocity of distance/time?
 
Yep. The reason is that the acceleration is uniform. Otherwise this isn't true.
 

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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...
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