Use the energy method to find the distance moved by particle

AI Thread Summary
The discussion focuses on using energy methods to calculate the distance moved by a particle in an A-level physics examination problem. The initial kinetic energy is calculated as 28.8 Joules, leading to the equation relating kinetic energy and gravitational potential energy. By solving for the vertical distance (h), it is determined to be 7.2 meters. Using the sine function for a 30-degree angle, the total distance traveled by the particle is found to be 14.4 meters. The calculations align with the mark scheme solution, confirming their accuracy.
chwala
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Homework Statement
A particle with mass ##0.4## kgs is projected with a speed of ##12## m/s up a line of greatest slope of a smooth plane inclined at ##30^0## to the horizontal.

i. Find the initial kinetic energy of the particle.

ii. Use an energy method to find the distance moved by the particle up the plane before coming to instantaneous rest.
Relevant Equations
kinetic energy
This is from an examination paper -A level. My interest is on part (ii). Ok my take;

i. ##KE_{initial} = \dfrac {1}{2} mu^2= \dfrac {1}{2}× 0.4 ×12^2=28.8## Joules.

ii. ##\dfrac {1}{2} mv^2=\dfrac {1}{2} mu^2-mgh##

##0=28.8-(0.4×10×h)## where h is the vertical perpendiculor distance.

##h=\dfrac{28.8}{4}=7.2##

It follows that;

##\sin 30^0=\dfrac{7.2}{s}##

##s=7.2×2=14.4## m

where ##s## is the distance travelled by the particle before coming to rest.

Your insight appreciated.

Mark scheme solution here

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Looks fine to me.
 
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