Two particles are projected from a point at the same instant with velocities whose horizontal components and vertical components are (u1 , v1) and (u2 , v2) respectively. The time interval between their passing through the other common point of their path (other than origin) is

Question

Two particles are projected from a point at the same instant with velocities whose horizontal components and vertical components are (u1 , v1) and (u2 , v2) respectively. The time interval between their passing through the other common point of their path (other than origin) is (A) (2/g)((v1 u1 - v2 u2/u1 + u2)) (B) (2/g)((v12 + v22/u1 + u2)) (C) (2/g)((u12 + u22/v1 + v2)) (D) (2/g)((v1 u2 - v2 u1/u1 + u2))

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-ujr1678hv5sv.png" /> The time for particle 1 to pass through common point of their path t1=(x/u1) The time for particle 2 to pass through common point of their path t2=(x/u2) Difference of time t=t1-t2 Time t=(x/u1)-(x/u2)=x((1/u1) - (1/u2)) y=xtanθ -(g x2/2 ux2) y=x(v1/u1)-(g x2/2 u12)=x(v2/u2)-(g x2/2 u22) (v1/u1)-(v2/u2)=x(g/2)((1/u12) - (1/u22)) (v1/u1)-(v2/u2)=x(g/2)((1/u1) + (1/u2))((1/u1) - (1/u2)) t=x((1/u1) - (1/u2))=(2/g)((v1 u2 - v2 u1/u1 + u2))

Q. Two particles are projected from a point at the same instant with velocities whose horizontal components and vertical components are $(u_{1}, v_{1})$ and $(u_{2}, v_{2})$ respectively. The time interval between their passing through the other common point of their path (other than origin) is

$\frac{2}{g} (\frac{v _{1} u _{1} - v _{2} u _{2}}{u _{1} + u _{2}})$

$\frac{2}{g} (\frac{v _{1}^{2} + v _{2}^{2}}{u _{1} + u _{2}})$

$\frac{2}{g} (\frac{u _{1}^{2} + u _{2}^{2}}{v _{1} + v _{2}})$

$\frac{2}{g} (\frac{v _{1} u _{2} - v _{2} u _{1}}{u _{1} + u _{2}})$

Q. Two particles are projected from a point at the same instant with velocities whose horizontal components and vertical components are (u1​,v1​) and (u2​,v2​) respectively. The time interval between their passing through the other common point of their path (other than origin) is

g2​(u1​+u2​v1​u1​−v2​u2​​)

g2​(u1​+u2​v12​+v22​​)

g2​(v1​+v2​u12​+u22​​)

g2​(u1​+u2​v1​u2​−v2​u1​​)

Q. Two particles are projected from a point at the same instant with velocities whose horizontal components and vertical components are $(u_{1}, v_{1})$ and $(u_{2}, v_{2})$ respectively. The time interval between their passing through the other common point of their path (other than origin) is

$\frac{2}{g} (\frac{v _{1} u _{1} - v _{2} u _{2}}{u _{1} + u _{2}})$

$\frac{2}{g} (\frac{v _{1}^{2} + v _{2}^{2}}{u _{1} + u _{2}})$

$\frac{2}{g} (\frac{u _{1}^{2} + u _{2}^{2}}{v _{1} + v _{2}})$

$\frac{2}{g} (\frac{v _{1} u _{2} - v _{2} u _{1}}{u _{1} + u _{2}})$