# How Do You Calculate the Radius of Curvature for a Projectile's Trajectory?

• Chantry09
In summary, the conversation is about a projectile being fired at an angle of 30 degrees with a velocity of 460 m/s. The question is to determine the radius of curvature of the trajectory at the position of the particle 10 seconds after firing. The suggested approach is to calculate the formula for y as a function of x, which should be a parabola, and then use that to calculate the curvature and finally the radius of curvature. The student is unsure of how to calculate curvature and asks for further explanation.
Chantry09

## Homework Statement

A projectile is fired at an angle of 30 degrees above the horinzontal with a velocity V0 of 460 m/s. Determine the radius of the curvature of the trajectory at the position of the particle 10 seconds after firing.

V = U + AT

## The Attempt at a Solution

By working out the speeds of the x and y components 10 seconds into the flight I've worked out the projectile is facing 39.466 degrees below the horizontal. However, now that i know the angle of the projectile 10 seconds into its journey, how do i work out the "radius of the curvature"?

Any help would be much appreciated.

James

You should have been able to calculate the precise formula for y as a function of x. (It should be a parabola.) Do you know how to calculate "curvature" from that? Radius of curvature is just the reciprocal of curvature.

I don't know how to calculate that, no. The teacher just said i had to work out the forces acting in the x and y direction at t=10 so that's what i did. If you could explain the next step or what i should have done that would be great.

## 1. What is the formula for calculating the angle of a projectile?

The formula for calculating the angle of a projectile is given by the inverse tangent of the vertical velocity divided by the horizontal velocity.

## 2. How do you find the maximum height of a projectile?

The maximum height of a projectile can be found by using the formula h = (v0sinθ)^2 / 2g, where v0 is the initial velocity, θ is the angle of the projectile, and g is the acceleration due to gravity.

## 3. What is the optimal angle for maximum range of a projectile?

The optimal angle for maximum range of a projectile is 45 degrees. This is because at this angle, the horizontal and vertical components of the initial velocity are equal, resulting in the longest possible range.

## 4. How does changing the angle affect the trajectory of a projectile?

Changing the angle of a projectile will affect its trajectory by altering the ratio of its horizontal and vertical velocities. A steeper angle will result in a shorter but higher trajectory, while a shallower angle will result in a longer but lower trajectory.

## 5. Can a projectile have multiple angles?

No, a projectile can only have one initial angle. However, once it is launched, factors such as air resistance and wind can affect its trajectory, causing it to change angles as it moves through the air.

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