How Long to Reach Maximum Height in Projectile Motion?

AI Thread Summary
To determine the time needed for a ball kicked at 40 m/s and 37 degrees to reach maximum height, the equations of motion are applied. The relevant equations include h = Voy t - 0.5 g t^2 and Vy = Voy - g t. The user derived two equations but initially struggled with two unknowns. By correctly applying the second equation, they calculated the time to be 2.4 seconds, which was confirmed as accurate. This demonstrates the effective use of projectile motion principles to solve for maximum height time.
RuthlessTB
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Homework Statement


A ball is kicked with initial velocity 40 m/s at an angle of 37 degree above the horizontal. What is the time (in seconds) needed to reach the maximum height?


Homework Equations


Y-axis
h= Voy t - 0.5 g t^2
Vy= Voy - g t
Vy^2= Voy^2 - 2 g h

X-axis
d= Vox t
Vx= Vox


The Attempt at a Solution


I reached to a point where I couldn't figure out a way to continue..

I used this equation
h= Voy t - 0.5 g t^2
h= (40 sin(37)) t - 5 t^2

I have 2 unknowns..
I tried to use Vy=Voy - g t
to find the time, I got so far these 2 equations
h= (40 sin(37)) t - 5 t^2
0=(40 sin(37)) - 10 t

Is this right?
 
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RuthlessTB said:

Homework Statement



I tried to use Vy=Voy - g t
to find the time, I got so far these 2 equations
h= (40 sin(37)) t - 5 t^2
0=(40 sin(37)) - 10 t
Is this right?
Yes, you can use either one to solve for t. If you use the upper formula, remember that you get the total flight time which you have to divide by 2 since we assume the projectile is symmetric.
 
Thank you, I used the second equation and the answer is 2.4 s.. is it right?
 
RuthlessTB said:
Thank you, I used the second equation and the answer is 2.4 s.. is it right?
Looks good.
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
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