(adsbygoogle = window.adsbygoogle || []).push({}); A particle is fired into the air with an initial velocity of 60m/s at an angle of 54 degrees from the ground. At time t=5.443, what is the radius of curvature of the path travelled by the particle?

I started by coming up with a vector equation for the path travelled by the particle, using the point of launch as the reference point.

[tex]

\overrightarrow r = (60t\cos 54)\widehat{\underline i } + (60t\sin 54 - 0.5g^2 )\widehat{\underline j }

[/tex]

The way i thought to approach this problem was to consider a circle which closely approximates the curve at the given instant.

For an infinitesimal change in time dt, the velocity along the path is given by:

[tex]

v = r\frac{{d\theta }}{{dt}}

[/tex]

I thought that perhaps if i could calculate the speed along the path v and the angular velocity, then i could use those to calculate the radius of curvature at that instant. I am able to calculate the speed easily, but not so sure about the angular velocity.

Am i on the right track, or should i be taking a different approach?

Thanks in advance,

Dan.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Radius of Curvature of particle

**Physics Forums | Science Articles, Homework Help, Discussion**