Calculating Height h from a Projectile Launched at A

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SUMMARY

The discussion focuses on calculating the height \( h \) of a projectile launched at point A with an initial velocity of 24 m/s at an angle of 60 degrees, impacting a vertical wall at point B. Participants clarify that the correct approach involves first determining the time \( t \) using the horizontal motion equations before substituting into the vertical motion equations to find \( h \). The assumption that vertical velocity \( v_y = 0 \) at the point of interest is incorrect, as it overlooks the need to calculate time based on horizontal displacement.

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Alexanddros81
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Homework Statement


A projectile launched at A with an initial velocity of 24 m/s at the angle θ=60deg, impacts the vertical wall at B. Neglecting air resistance, calculate the height h

Homework Equations

The Attempt at a Solution


Here is my solution

Pytel_Dynamics038.jpg


Pytel_Dynamics039.jpg
As you can see to find height h I assumed that ##v_y=0## in the second of Eqs. (f) and solved for time.
Is this correct or should I have solved first equation of (g) to find time and then solve for y?
 
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Alexanddros81 said:
I assumed that ##v_y=0##
Then don't. There is no basis for such an assumption.
Yes, find t first.
 
Look at your equations labeled (e). The first equation can be used to find an expression for t in terms of x and θ. Substitute that in the second equation and you will have y as a function of x and θ. Substitute the given numbers for x and θ to find h.
 
Pytel_Dynamics043.jpg


Can you check this?
 
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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