Projectile Motion comparing height and initial velocity

In summary, the conversation discusses a question about two projectiles launched at the same angle and the ratio of their initial speeds. The participant suggests a formula and explains their reasoning, but is corrected by the other person. They then discuss an alternative formula that relates max height with initial velocity without the need for time, and confirm that the answer is correct as root(2).
  • #1
DarkBlitz
22
0
Hey,
I came across this question in my textbook, and there isn't an answer for it in the back, so I would just like to check if I have my head around it.

The question is:
2 projectiles are launched at the same angle. Projectile 1 reaches a max height of twice that of the projectile 2. What is the ration of the initial speeds?

I said that they where in the ratio 4:1, as one of the formulas is: y=yo +voyt -0.5gt^2
and because the height is doubled, the time taken must also be doubled?
am I correct in saying this?

Thanks
 
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  • #2
DarkBlitz said:
I said that they where in the ratio 4:1, as one of the formulas is: y=yo +voyt -0.5gt^2
and because the height is doubled, the time taken must also be doubled?
am I correct in saying this?
No.

Come up with a formula that relates max height with initial velocity without the need for the time.
 
  • #3
I got an answer or root(2), is this correct?
 
  • #4
DarkBlitz said:
I got an answer or root(2), is this correct?
Yes.
 
  • #5
Thank you very much!
 

1. What is Projectile Motion?

Projectile motion is the motion of an object through the air, under the force of gravity, after it has been launched at an angle. This type of motion follows a curved path known as a parabola.

2. How does initial velocity affect the height of a projectile?

The initial velocity, or the speed and direction at which an object is launched, directly affects the height of a projectile. The higher the initial velocity, the higher the projectile will go before falling back to the ground.

3. What happens to the height of a projectile if the initial velocity is doubled?

If the initial velocity is doubled, the height of the projectile will also be doubled. This is because the initial velocity has a direct impact on the maximum height a projectile can reach.

4. How does the angle of launch affect the height of a projectile?

The angle of launch, also known as the angle of elevation, determines the shape of the projectile's trajectory and thus affects its height. A higher angle of launch will result in a higher maximum height, while a lower angle will result in a lower maximum height.

5. Is there a relationship between the initial velocity and the maximum height of a projectile?

Yes, there is a direct relationship between the initial velocity and the maximum height of a projectile. As the initial velocity increases, the maximum height also increases. This relationship can be described by the equation h = (v^2 sin^2θ)/g, where h is the maximum height, v is the initial velocity, θ is the angle of launch, and g is the acceleration due to gravity.

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