Projectile Motion (find theta)

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Homework Help Overview

The problem involves determining the initial projection angle of a projectile based on the relationship between its speeds at maximum height and half of that height. The context is projectile motion, specifically focusing on the kinematic equations related to height and range.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to establish a ratio between the speeds at different heights but expresses difficulty in starting the solution. Some participants suggest decomposing the velocity vector and relating components of velocity at maximum height to the given information.

Discussion Status

The discussion is ongoing, with participants exploring different approaches to the problem. Some guidance has been offered regarding the decomposition of the velocity vector and its implications for the problem setup. There is no explicit consensus yet, as participants are still working through their reasoning.

Contextual Notes

There is mention of the original poster's struggle with initial steps and a delay in responses due to lectures, indicating potential constraints on engagement and time management.

bengavinb20
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Homework Statement



The speed of a projectile when it reaches its maximum height is 0.31 times its speed when it is at half its maximum height. What is the initial projection angle of the projectile?

Homework Equations



h=(Vi^2 * sin^2 θ) / 2g

R=(Vi^2 * sin2θ) / g

The Attempt at a Solution



I realize that i need to somehow come up with a ratio and set the two equal to each other. However, I'm having difficulty with the initial step. Maybe I could get a hint that could set me on the right track?
 
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Decompose the velocity vector.
At the top which component of velocity is zero?
Use this idea to find the ratio. As you mentioned
 
So after decomposing the velocity vector I got:

Vi = -yf-at2 /t

Plugging that into the equation for h...

h= ((-yf-at2)2*(sin2θ)) / 2g

and then

0.5h = 0.31((-yf-at2)2*(sin2θ)) / 2g

Am I on the right track?
 
You see at the top point V is just Vx so can you relate this to the given information.
 
I'm sorry for late response I got lectures :)
So you still solving the problem?
 

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