Question

Two identical particles are projected horizontally in opposite directions with a speed of 5 ms1 each from the top of a tall tower as shown. Assuming g = 10 ms2, the distance between them at the moment when their velocity vectors become mutually perpendicular is

Answer 1

Hey Dear,

◆ Answer -

t = 1/2 s = 0.5 s

◆ Explanation -

Let u & v (in vector form) be velocities of two particles such that -

u = ux + uy

v = vx + vy

Let the velocities are perpendicular at time t.

ux = 5 m/s

uy = gt = 10t

vx = -5 m/s

vy = gt = 10t

Velocities are perpendicular at time t, this can be written as -

u.v = 0

(5 + 10t).(-5 + 10t) = 0

-25 + 100t² = 0

t² = 25 / 100

t = 1/2 s = 0.5 s

Therefore, the particles will have mutually perpendicular velocities after 0.5 s.

Hope this is useful..