Maximum height of a projectile

In summary, the maximum height of a projectile, H, divided by the range of the projectile, R, is equal to 1/4 tan when calculated using the kinematics equations for horizontal and vertical displacement in terms of velocity (v) and angle (theta).
  • #1
dg_5021
80
0
Prove that the maximum height of a projectile H, divided by the range of the projectile, R, satisfies the relation H/R = 1/4 tan.


I have no idea how to do this
 
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  • #2
Why don't you start by figuring out what happens to a projectile at its max heights and then find a mathematical relationship for that. Then do the same for the range, and see what you can come up with.
 
  • #3
what happens to a projectile at its max heights ?
 
  • #4
Calculate the height in terms of v which is the speed, and theta which is the angle.

Calculate the range in terms of v and theta.

Take the ratio, and the result follows.

To get the range and height... begin by writing the 2 kinematics equations (that give horizontal and vertical displacement for any time)
 

Related to Maximum height of a projectile

1. What is the maximum height of a projectile?

The maximum height of a projectile is the highest point that it reaches during its flight.

2. How is the maximum height of a projectile calculated?

The maximum height of a projectile is calculated using the equation: h = (v^2 * sin^2θ) / 2g, where h is the maximum height, v is the initial velocity, θ is the launch angle, and g is the acceleration due to gravity.

3. Does air resistance affect the maximum height of a projectile?

Yes, air resistance can affect the maximum height of a projectile. It can decrease the maximum height by slowing down the projectile's speed and reducing its vertical acceleration.

4. What factors can affect the maximum height of a projectile?

The maximum height of a projectile can be affected by factors such as the initial velocity, launch angle, air resistance, and the acceleration due to gravity.

5. How can the maximum height of a projectile be increased?

The maximum height of a projectile can be increased by increasing the initial velocity, launching the projectile at a higher angle, or reducing the effects of air resistance.

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