Find max height of inclined plane

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A block with an initial velocity of 2 m/s is projected up a frictionless incline at a 60-degree angle, and the goal is to determine the maximum height reached. The initial calculations involved finding the block's velocity component along the incline and the acceleration due to gravity. The user initially attempted to use kinematic equations to find the height but received an incorrect answer of 0.24 m. It was clarified that the problem actually seeks the displacement along the slope rather than the vertical height. The discussion emphasizes the importance of correctly interpreting the problem and suggests using conservation of energy for a more straightforward solution.
Ilovepysics
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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:
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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