Projectile at 1/4 height

In summary, at the maximum height of a projectile, the speed is 1/4 of the speed when the projectile is at 1/4 its maximum height.
  • #1
pereus
3
0

Homework Statement


The speed of a projectile when it reaches its maximum height is 1/4 the speed when the projectile is at 1/4 its maximum height.
What is the initial projection angle?
Answer in units of ◦

Homework Equations


v2 = v02 + 2a(delta s)
4Vx = v1/4

The Attempt at a Solution


I've tried substituting v1/4 for 4vx and some other things, but I lost those papers.
 
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  • #2
pereus said:

Homework Statement


The speed of a projectile when it reaches its maximum height is 1/4 the speed when the projectile is at 1/4 its maximum height.
What is the initial projection angle?
Answer in units of ◦

Homework Equations


v2 = v02 + 2a(delta s)
4Vx = v1/4

The Attempt at a Solution


I've tried substituting v1/4 for 4vx and some other things, but I lost those papers.

What is the significance of the speed at maximum height? What is the velocity at maximum height?
 
  • #3
I know that the velocity at the top is Vx. That is how I was able to make 4vx = to 4v1/4
 
  • #4
pereus said:
I know that the velocity at the top is Vx. That is how I was able to make 4vx = to 4v1/4

What do you mean by Vx ? What is significant at the top?
 
  • #5
At the top the projectile is moving with the velocity Vx which is equal to v0cos(theta). There is no velocity in the y direction
 
  • #6
pereus said:
At the top the projectile is moving with the velocity Vx which is equal to v0cos(theta). There is no velocity in the y direction

OK.

You can actually analyse the second half of the projectile flight, as it mirrors the first [going down and going up work the same numerically] however.

At 1/4 the max height, there will be a vertical component to the velocity, and application of Pythagorus will enable you to find that, since the result is 4Vx.
You will get the vertical component in terms of Vx, but you are only using it to find an angle.
Once you have the vertical vel 1/4 way up - or if you like, 3/4 way down, you can find it at the beginning / end and again use trig to find the angle.

You could actually be using Potential Energy / Kinetic Energy / Total Energy to be working this out.
 

1. What is a projectile at 1/4 height?

A projectile at 1/4 height refers to an object that is launched or thrown into the air at an angle and reaches a height that is 1/4 of its maximum height before falling back to the ground.

2. How is the height of a projectile at 1/4 height calculated?

The height of a projectile at 1/4 height can be calculated using the formula h = (1/4) * (v^2/g), where h is the height, v is the initial velocity, and g is the acceleration due to gravity.

3. What factors affect the height of a projectile at 1/4 height?

The height of a projectile at 1/4 height is affected by the initial velocity, launch angle, and the acceleration due to gravity.

4. How does air resistance impact a projectile at 1/4 height?

Air resistance can reduce the height of a projectile at 1/4 height by slowing down its speed and reducing its maximum height. This is because air resistance creates a force that acts against the motion of the projectile.

5. How can the height of a projectile at 1/4 height be increased?

The height of a projectile at 1/4 height can be increased by increasing the initial velocity, increasing the launch angle, or reducing the effects of air resistance. This can be achieved by using a more aerodynamic projectile or launching it in an environment with less air resistance, such as in a vacuum.

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