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

Question

Two particles are projected simultaneously from the level ground as shown in figure. They may collide after a time: (A) (x sin θ2/u1) (B) (x cos θ2/u2) (C) (x sin θ2/u1 sin (θ2-θ1)) (D) (x sin θ1/u2 sin (θ2-θ1))

Tardigrade Admin · Accepted Answer

x+u2 cos θ2 t=u1 cos θ1 t ∴ t=(x/u1 cos θ1-u2 cos θ2) ..........(i) text Also u1 sin θ1=u2 sin θ2...........(ii) After solving above equations, we get t=(x sin θ2/u1 sin (θ2-θ1))

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

$\frac{x s i n θ _{2}}{u _{1}}$

$\frac{x c o s θ _{2}}{u _{2}}$

$\frac{x s i n θ _{2}}{u _{1} s i n ( θ _{2} - θ _{1} )}$

$\frac{x s i n θ _{1}}{u _{2} s i n ( θ _{2} - θ _{1} )}$

$x + u_{2} cos θ_{2} t = u_{1} cos θ_{1} t$
$∴ t = \frac{x}{u _{1} c o s θ _{1} - u _{2} c o s θ _{2}}$ ..........(i)
$Also u_{1} sin θ_{1} = u_{2} sin θ_{2}$ ...........(ii)
After solving above equations, we get
$t = \frac{x s i n θ _{2}}{u _{1} s i n ( θ _{2} - θ _{1} )}$

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

u1​xsinθ2​​

u2​xcosθ2​​

u1​sin(θ2​−θ1​)xsinθ2​​

u2​sin(θ2​−θ1​)xsinθ1​​

x+u2​cosθ2​t=u1​cosθ1​t ∴t=u1​cosθ1​−u2​cosθ2​x​..........(i) Also u1​sinθ1​=u2​sinθ2​...........(ii) After solving above equations, we get t=u1​sin(θ2​−θ1​)xsinθ2​​

$\frac{x s i n θ _{2}}{u _{1}}$

$\frac{x c o s θ _{2}}{u _{2}}$

$\frac{x s i n θ _{2}}{u _{1} s i n ( θ _{2} - θ _{1} )}$

$\frac{x s i n θ _{1}}{u _{2} s i n ( θ _{2} - θ _{1} )}$

$x + u_{2} cos θ_{2} t = u_{1} cos θ_{1} t$
$∴ t = \frac{x}{u _{1} c o s θ _{1} - u _{2} c o s θ _{2}}$ ..........(i)
$Also u_{1} sin θ_{1} = u_{2} sin θ_{2}$ ...........(ii)
After solving above equations, we get
$t = \frac{x s i n θ _{2}}{u _{1} s i n ( θ _{2} - θ _{1} )}$