Home
Class 11
PHYSICS
If at point of projection , the velcoi...

If at point of projection , the velcoity of particle is "u" and is direction at an angle `alpha` to the horizontal , then show that it will be moving at right angles to the its initial direction after a time `((u "cosec" alpha))/(g)`

Text Solution

Verified by Experts

Let t be the time after which velocity becomes perpendicular to its initial direction.
As u and v are perpendicular the angle between v and vertical will be `alpha`
Intitial velocity `u=(u cos alpha hati+u sin alpha hatj)`
After t sec velocity `v={u cos alpha hati +(usin alpha-"gt")hatj}`
`:.` These are perpendicular their dot product is zero
`:.(ucos alpha i+usin j).{ucos alphai+(usin alpha-"gt")j}=0`
and `t=(u cosec alpha)/g`
Promotional Banner

Similar Questions

Explore conceptually related problems

A particle is projected from a point P with a velocity v at an angle theta with horizontal. At a certain point Q it moves at right angles to its initial direction. Then

A particle is projected from a point P with a velocity v at an angle theta with horizontal. At a certain point Q it moves at right angles to its initial direction. Then

If any point of a parabolic path of a projectile the velocity be u and the dirrection of motion be at theta with the horizon , show that the particle is moving at right angle to its former direction after an interval of time t = (u)/(g sin theta)

A particle is projected from a point O with velocity u in a direction making an angle alpha upward with the horizontal. AT P , it is moving at right angles to its initial direction of projection . Its velocity at P is .

A particle of mass m is projected at an angle alpha to the horizontal with an initial velocity u . The work done by gravity during the time it reaches its highest point is

A particle is projected at an angle theta with an initial speed u .

A body is projected with a velocity u at an angle of 60^(@) to the horizontal. The time interval after which it will be moving in a direction of 30^(@) to the horizontal is

A particle is thrown with a speed u at an angle theta with the horizontal. When the particle makes an angle phi with the horizontal. Its speed changes to v :

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 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.