Projection angle using max. height w/ proportions only

In summary, the problem involves finding the initial projection angle of a projectile given that its speed at maximum height is half of its speed at half its maximum height. The relevant equation is h = (vi^2 sin^2 theta)/2g and the attempt at a solution involves breaking velocity into x and y components and using the formula for speed (sqrt of the sum of the squares).
  • #1
amphiprion86
1
0
Figures that the only problem I have trouble with is the one the book considers to be "easy":

Homework Statement


The speed of a projectile when it reaches its maximum height is one half 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 theta)/2g


The Attempt at a Solution



Complete brain fart--I don't even know where to start, beyond trying to divide h/2, which would be (vi^2 sin^2 theta)/4g, correct? That's about as far as I got. I just keep miring myself the further into it I go.
 
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  • #2
Speed of course is the magnitude of velocity. At its maximum height a projectile only has one component of velocity. Is that enough to get you started?
 
  • #3
Try breaking velocity into x and y components @ 1/2 max height and then finding speed from there the "sqrt of the sum of the squares".
 

Related to Projection angle using max. height w/ proportions only

1. What is the formula for calculating projection angle using maximum height with proportions only?

The formula for calculating projection angle using maximum height with proportions only is: θ = arctan(2h/h), where θ is the projection angle and h is the maximum height.

2. Can I use this formula for any type of projectile?

Yes, this formula can be used for any type of projectile as long as you know the maximum height reached and the horizontal distance traveled.

3. How do I determine the maximum height of a projectile?

The maximum height of a projectile can be determined by finding the highest point on the projectile's trajectory. This can be done by using the formula h = (v₀sinθ)²/2g, where h is the maximum height, v₀ is the initial velocity, θ is the projection angle, and g is the acceleration due to gravity.

4. Do I need to know the initial velocity to calculate the projection angle using maximum height with proportions only?

Yes, the initial velocity is required to calculate the projection angle using maximum height with proportions only. If you do not know the initial velocity, you can use the formula θ = arctan(2h/gt²) to calculate the projection angle, where t is the time it takes for the projectile to reach its maximum height.

5. Can I use this formula to calculate the projection angle for a projectile launched from an elevated position?

Yes, you can use this formula to calculate the projection angle for a projectile launched from an elevated position. However, you will need to take into account the elevation angle in addition to the maximum height and horizontal distance traveled when using the formula.

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