Question

Find the time after which the velocity of a projectile become perpendicular to its initial velocity.


The answer is u/g.sin∅.
I want the explanation for it.​

Answer 1

when initial and final velocity becomes perpendicular then their dot product must be zero.

Answer 2

Answer: Time after which the velocity of a projectile become perpendicular to its initial velocity is u/g.sin(Ф)

Explanation:

Step 1 : Choosing reference frame and set of axis.

Let the point on ground from where body is projected be origin.

X axis in direction of initial velocity and Y axis perpendicular to x axis.

Step 2 : Breaking acceleration of gravity into components along X and Y axis.

a = - gsin(Ф) i - gcos(Ф) j

Step 3: Writing velocity at general time t

v = u + at

u = u i

v =  u i + (- gsin(Ф) i - gcos(Ф) j ) t

v = ( u -  gsin(Ф) t ) i  - (gcos(Ф)t) j

When final velocity becomes perpendicular to initial velocity, final velocity will be in direction of Y axis. Therefore, i component of velocity will be 0.

u -  gsin(Ф) t  = 0

gsin(Ф) t = u

t = u/g.sin(Ф)

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