Q20 of 43 Page 85

A particle is projected with a velocity u at an angle θ° with the horizontal at any instant. Its velocity v is at right angles to its initial velocity u then v is

(a) u cos θ°


(b) u tan θ°


(c) u cot θ°


(d) u sec θ°

u = Velocity of projection

Ɵ = Angle of Projection


= Initial velocity along x axis


= Initial velocity along y axis


= Acceleration along x axis


= Acceleration along y axis


Using equations of motion:




At any instantaneous time, ‘t’ the angle that v makes with the horizontal is.


So, …3


Given that v makes angle 90° with u,




…4


Now,


So,





…5


Now,



(From 5) …6


Similarly,


(From 5)



…7


Now, ..8


(Putting 6,7 in 8)



…9


Putting 5 in 9, we get:




More from this chapter

All 43 →
18

A swimmer crosses the river along the line making an angle 45° with the direction of flow of the river. If the velocity of river is 5 ms–1 and time taken by him is 6 seconds to cross the width of river 60m, then find the velocity of swimmer w.r.t. to the river.

 19

The resultant of two vectors at angle 150° is 10 units and is perpendicular to one vector. The magnitude of the smaller vector is

 21

Rain is falling vertically with a speed of 35 ms–1. A woman rides a bicycle with a speed of 12 ms–1 in the east to west direction. In which direction should she hold her umbrella?

 22

A particle is projected upwards. The times corresponding to height h while ascending and descending are t1 and t2 respectively. Find the velocity of projection.