Find max height of inclined plane

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SUMMARY

The discussion centers on calculating the maximum height reached by a block on a frictionless inclined plane at a 60-degree angle, given an initial velocity of 2 m/s. The participant initially used kinematic equations but arrived at an incorrect height of 0.24 m. The correct approach involves recognizing that the problem seeks the displacement along the slope, not the vertical height. The hint provided emphasizes the use of conservation of energy and suggests simplifying the analysis by utilizing the kinematic equation v² = u² + 2ad.

PREREQUISITES
  • Understanding of kinematic equations, specifically v² = u² + 2ad
  • Knowledge of trigonometric functions, particularly sin(θ)
  • Familiarity with the concept of conservation of energy in physics
  • Ability to analyze motion on an inclined plane
NEXT STEPS
  • Study the application of conservation of energy in inclined plane problems
  • Learn how to derive and use kinematic equations effectively
  • Explore the properties of special triangles, especially 30-60-90 triangles
  • Practice problems involving motion on inclined planes to solidify understanding
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and inclined plane problems, as well as educators seeking to clarify concepts related to motion and energy conservation.

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1. Homework Statement
A block given an intial velocity of 2m/s up a frictionless inclined at 60 degrees to the horizontal. What is the highest point reached by the block?


2. Homework Equations

gsin(θ)=a
a=v/t
d=vit + 1/2at^2

3. The Attempt at a Solution
Found vx = vsin60= 2(sin60)=1.73

I solved for the acceleration
10(sin60)= 8.66 m/s^2

Then I found time using v/t=a

Then plugged in the time t into
d=vit+1/2at^2

Then used sin60= Opposite/hypotonuse to solve for the height.

But I did not get the correct answer of .24m. Can someone tell me where I am going wrong and point me in the right direction please
 
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Hint: Conservation of energy.

(note: you overcomplicated your analysis by doing too many steps - to use kinematics, you want to draw the v-t graph for the motion - it's a triangle - use this to get equations for displacement and acceleration which will be two equations with two unknowns. eg. make the final equation before you plug the numbers in. The kinematic equation you were looking for was v^2=u^2+2ad, saves wear and tear on your calculator to notice that sin(60)=(√3)/2 - watch for these special triangles.)

[edit]
I got it - the problem is not looking for the height the "correct" answer appears to be for the displacement along the slope.
 
Last edited:

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