Question

Two particles are projected simultaneously from the level ground as shown in figure. They may collide after a time:

Options

• `(x  sin theta_2)/"u"_1` 

• `(x  sin theta_2)/"u"_2` 

• `(x  sin theta_2)/("u"_1sin (theta_2-theta_1))` 

• `(x  sin theta_2)/("u"_2sin (theta_2-theta_1))` 

Answer 1

`bb((x  sin theta_2)/("u"_1sin (theta_2-theta_1)))` 

Explanation:

If the two projected particles are in the same position at the same time, they will collide.

t = `x /("u"_1cos theta_1-"u"_2cos theta_2)`        ...(i)

And u₁ sin θ₁ . t - `1/2`gt² = u₂ sin θ₂ . t - `1/2`gt²

∴  u₁ sin θ₁ = u₂ sin θ₂      ...(ii)

from equation no. (i) & (ii)

t = `x/"u"_1cos theta_1-("u"_1sin theta_1.costheta_2)/sintheta_2`

∴ t = `(x  sin theta_2)/("u"_1sin (theta_2-theta_1))`