(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A very small steel marble is shown rolling at a constant speed on a horizontal table. The marble leaves the table at L, falls, and hits the ground at P. This is illustrated in the diagram below which is drawn to scale. Calculate the time it took the marble to travel from N to P.

Please look at the graph:

http://i995.photobucket.com/albums/af79/huybinhs/plot.png

2. Relevant equations

p(t) = 0.5 * a * t^2 + v0 * t + p0

where

p(t) is position at time t

a is acceleration

v0 is initial velocity at time 0

p0 is position at time 0

3. The attempt at a solution

p(t) = 0.5 * a * t^2 + v0 * t + p0

where

p(t) is position at time t

a is acceleration

v0 is initial velocity at time 0

p0 is position at time 0

We'll use the fall from L to P to compute v0.

Vertical acceleration due to gravity = -9.8 m/s^2 = -980 cm/s^2

Let t = 0 when the marble is at point L.

horizonatal

px(t) = 100 = 0.5 * 0 * t^2 + v0 * t + 50 = v0 * t + 50

vertical

py(t) = 0 = 0.5 * -980 * t^2 + 0 * t + 90 = -490 * t^2 + 90

Two equations. Two Unknowns. Solve for t and v0.

=> t1 = 0.43; v0= 116.28

To find the time need to travel from point N to L use v0 from above

px(t) = 50 = 0.5 * 0 * t^2 + v0 * t + 10 = v0 * t + 10

=> t2 = 0.34

Add the two times for the total time from L to P.

=> t = t1+t2= 0.774 which came out wrong. I dont know why???? Please help and let me know the result!!!

Thanks so much!

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# Homework Help: Calculate the time it took the marble to travel from N to P?

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