Grade 11Mechanics

A particle is projected with velocity u at angle theta with horizontal find the time when velocity vector is perpendicular to intial velocity vector

G .harrish

7 Years agoGrade 11

2 Answers

Eshan

7 Years ago

Piyush Kumar Maurya

7 Years ago

Initial velocity = u

u = u_x+ u_y

u = ucos theta i cap+ usin theta j cap

Here u_xremains constant throughout the journey.

Velcity at time t = v

V_x= ucos theta

V_y= usin theta - gt

V(t) = ucos theta i cap + (usin theta - gt) j cap

Now for V(t) to be perpendicular to u , their dot product should be zero.

So , V(t) . u = 0

[ ucos theta i cap + ( usin theta - gt) j cap] . (ucos theta i cap + usin theta j cap) = 0

> u²cos^2 theta + u²sin^2 theta - usin theta *gt = 0

> t= u / sin theta *g

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A particle is projected with velocity u at angle theta with horizontal find the time when velocity vector is perpendicular to intial velocity vector

G .harrish

2 Answers

Eshan

Piyush Kumar Maurya

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