Home
Class 11
PHYSICS
A particle is projected with a velocit...

A particle is projected with a velocity `bar(v) = ahat(i) + bhat(j)` . Find the radius of curvature of the trajectory of the particle at (i) point of projection (ii) highest point .

Text Solution

Verified by Experts

(i) Let the angle of projection be `theta`
At the point of projection `P,a_(n)=gcos theta_(0)`
Hence the radius of curvature at P is `r_(p)=(v_(p)^(2))/(alpha_(n))=(v_(0)^(2))/(g cos theta_(0))`
Since `tan theta_(0)=b//a,cos theta_(0)=a/(sqrt(a^(a)+b^(2)))`
Substituting `v_(0)=sqrt(a^(2)+b^(2))` and `cos theta_(0)=a/(sqrt(a^(2)+b^(2)))`, we have `r-(p)=(a^(2)+b^(2))^(3//2)g//a`
(ii) At the highest position Q, the velocity of the particle is `v_(Q)=v_(0)cos theta_(0)`
Since it moves horizontally at highest point `Q.veca_(n)=vec(g) (_|_ vecv)`
Hence the radius of curvature at Q is
`r_(Q)=(v_(Q)^(2))/(a_(n))=(v_(0)^(2)cos^(2)theta)/g`

Where `v_(0)cos theta=v_(x)=a` (given)
Then `r_(Q)=(a^(2))/g`
Promotional Banner

Similar Questions

Explore conceptually related problems

A particle is projected with speed u at angle theta to the horizontal. Find the radius of curvature at highest point of its trajectory

A particle is projected with a speed u at an angle theta to the horizontal. Find the radius of curvature. At the point where the particle is at a highest half of the maximum height H attained by it.

A particle is projected with velocity 20 ms ^(-1) at angle 60^@ with horizontal . The radius of curvature of trajectory , at the instant when velocity of projectile become perpendicular to velocity of projection is , (g=10 ms ^(-1))

A particle is projected with a velocity 10 m//s at an angle 37^(@) to the horizontal. Find the location at which the particle is at a height 1 m from point of projection.

A particle is projected from the ground with an initial speed v at an angle theta with horizontal. The average velocity of the particle between its point of projection and highest point of trajectory is [EAM 2013]

A particle of mass m is projected with speed u at an angle theta with the horizontal. Find the torque of the weight of the particle about the point of projection when the particle is at the highest point.

A particle of mass m is projected with speed u at an angle theta with the horizontal. Find the torque of the weight of the particle about the point of projection when the particle is at the highest point.

A particle is projected with velocity v at an angle theta aith horizontal. The average angle velocity of the particle from the point of projection to impact equals

A heavy particle is projected with a velocity at an angle with the horizontal into the uniform gravitational field. The slope of the trajectory of the particle varies as

A particle of mass m is projected with a velocity v making an angle of 45^@ with the horizontal. The magnitude of the angular momentum of the projectile abut the point of projection when the particle is at its maximum height h is.