What Is the Initial Speed of a Ball Thrown at an Angle to Return in 3 Seconds?

AI Thread Summary
To determine the initial speed of a ball thrown at a 36.0° angle that returns to its original level in 3 seconds, focus on the vertical motion. The final velocity at the peak is zero, and the time to reach this height is half of the total time, which is 1.5 seconds. Using the equation v = u + at, where 'a' is the acceleration due to gravity, you can calculate the initial vertical velocity. This vertical component can then be used to find the overall initial speed by resolving it with the angle of projection. The calculations will yield the required initial speed for the ball.
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Homework Statement



A ball thrown straight upward returns to its original level in 3.00 s. A second ball is thrown at an angle of 36.0° above the horizontal. What is the initial speed of the second ball if it also returns to its original level in 3.00 s?
anwer : ___ m/s


Homework Equations



i need help finding the correct equation which would guide me to a correct answer

The Attempt at a Solution

 
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Consider the vertical motion of the particle. You know that v=u+at. Take the final velocity v to be zero (at the maximum height of the particle, and halfway through the motion). You know the time t (half of the total time), and the acceleration due to gravity. This let's you find the initial vertical velocity of the particle, which you can then resolve to find the initial speed. Hope that makes sense and helps!
 
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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