Two particles are projected simultaneously with same speed V0 in same vertical plane at angles 30o and 60o with the horizontal. The time at which their velocities becomes parallel is

Question

Two particles are projected simultaneously with same speed V0 in same vertical plane at angles 30o and 60o with the horizontal. The time at which their velocities becomes parallel is (A) (V0/2 g) (B) V0((√3 + 1/2 g)) (C) (√3 V0/2 g) (D) (V0 (√3 - 1)/g)

Tardigrade Admin · Accepted Answer

overset arrow V1=V0cos (30)o hati+(V0 sin â¡ (30)o - g t) hatj overset arrow V2=V0cos (60)o hati+(V0 sin â¡ (60)o - g t) hatj ∵ overset arrow V1|.|. overset arrow V2 ⇒ (V0 cos 30o/V0 cos â¡ 60o)=(V0 sin â¡ 30o - g t/V0 sin â¡ 60o - g t) ⇒ t=(V0 (√3 + 1)/2 g)

Q. Two particles are projected simultaneously with same speed $V_{0}$ in same vertical plane at angles $3 0^{o}$ and $6 0^{o}$ with the horizontal. The time at which their velocities becomes parallel is

$\frac{V _{0}}{2 g}$

$V_{0} (\frac{3 + 1}{2 g})$

$\frac{3 V _{0}}{2 g}$

$\frac{V _{0} ( 3 - 1 )}{g}$

Q. Two particles are projected simultaneously with same speed V0​ in same vertical plane at angles 30o and 60o with the horizontal. The time at which their velocities becomes parallel is

2gV0​​

V0​(2g3​+1​)

2g3​V0​​

gV0​(3​−1)​

V1​→​=V0​cos(30)oi^+(V0​sin⁡(30)o−gt)j^​ V2​→​=V0​cos(60)oi^+(V0​sin⁡(60)o−gt)j^​ ∵V1​→​∣∣V2​→​ ⇒V0​cos⁡60oV0​cos30o​=V0​sin⁡60o−gtV0​sin⁡30o−gt​ ⇒t=2gV0​(3​+1)​

Q. Two particles are projected simultaneously with same speed $V_{0}$ in same vertical plane at angles $3 0^{o}$ and $6 0^{o}$ with the horizontal. The time at which their velocities becomes parallel is

$\frac{V _{0}}{2 g}$

$V_{0} (\frac{3 + 1}{2 g})$

$\frac{3 V _{0}}{2 g}$

$\frac{V _{0} ( 3 - 1 )}{g}$