What Was Johnny's Initial Speed Sliding Down the Slope?

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SUMMARY

To determine Johnny's initial speed sliding down a 20-degree slope, the correct calculations involve understanding the forces acting on him. The net force equation is established as mgsin(20) - 0.5mgcos(20) = ma. After correctly calculating the acceleration as 2.88 m/s², the initial speed can be derived using the kinematic equation Vi² = 0 + 2(-2.88)(3.5), resulting in an initial speed of 2.96 m/s. The initial miscalculation stemmed from an error in the acceleration calculation.

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Johnny jumps off a swing, lands sitting down on a grassy 20 degree slope, and slides 3.5 m down the slope before stopping. The coefficient of kinetic friction between grass and the seat of Johnny's pants is 0.5.What was his initial speed on the grass?

now i know the answer is 2.96m/s, but i don't know how to get at it...heres what i tried:

Fn= mgsin20

Ff=.5mgcos20

mgsin20-Ff= ma

mgsin20- .5mgcos20 = ma

(m's cancel out)
a=2.88 m/s^2

Vi^2= 0 + 2(-2.88)(3.5)
Vi= 4.49 m/s

but this is definitely wrong... how do i get the real answer?
 
Last edited:
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nick727kcin said:
heres what i tried:

Fn= mgsin20

Ff=.5mgcos20

mgsin20-Ff= ma

mgsin20- .5mgcos20 = ma

(m's cancel out)
a=2.88 m/s^2
Your method is perfect, but redo the calculation for "a".
 
thank you, my friend :biggrin:
 

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