Two particles A and B start moving with velocities 20 m / s and 30 √2 m / s along x-axis and at an angle 45° with x-axis respectively in x y-plane from origin. The relative velocity of B w.r.t. A

Question

Two particles A and B start moving with velocities 20 m / s and 30 √2 m / s along x-axis and at an angle 45° with x-axis respectively in x y-plane from origin. The relative velocity of B w.r.t. A (A) (10 hati+30 hatj) m / s (B) (30 hati+10 hatj) m / s (C) (30 hati-20 √2 hatj) m / s (D) (30 √2 hati+10 √2 hatj) m / s

Tardigrade Admin · Accepted Answer

vA=20 m / s vB=30 √2 m / s along 45° with x-axis vecvB=vB cos 45° hati+vB sin 45° hatj=30 hati+30 hatj vecvB A= vecVB- vecVA=30 hati+30 hatj-20 hati vecvB A=10 hati+30 hatj

Q. Two particles $A$ and $B$ start moving with velocities $20 m / s$ and $302 m / s$ along $x$ -axis and at an angle $4 5^{\circ}$ with $x$ -axis respectively in $x y$ -plane from origin. The relative velocity of $B$ w.r.t. $A$

$(10 \hat{i} + 30 \hat{j}) m / s$

$(30 \hat{i} + 10 \hat{j}) m / s$

$(30 \hat{i} - 202 \hat{j}) m / s$

$(302 \hat{i} + 102 \hat{j}) m / s$

$v_{A} = 20 m / s$
$v_{B} = 302 m / s$ along $4 5^{\circ}$ with $x$ -axis
$v_{B} = v_{B} cos 4 5^{\circ} \hat{i} + v_{B} sin 4 5^{\circ} \hat{j} = 30 \hat{i} + 30 \hat{j}$
$v_{B A} = V_{B} - V_{A} = 30 \hat{i} + 30 \hat{j} - 20 \hat{i}$
$v_{B A} = 10 \hat{i} + 30 \hat{j}$

Q. Two particles A and B start moving with velocities 20m/s and 302​m/s along x-axis and at an angle 45∘ with x-axis respectively in xy-plane from origin. The relative velocity of B w.r.t. A

(10i^+30j^​)m/s

(30i^+10j^​)m/s

(30i^−202​j^​)m/s

(302​i^+102​j^​)m/s