Ship A is sailing towards north-east with velocity) overset arrow v=30 hati+50 hatjkmh- 1 where hati points east and hatj, north. The ship B is at a distance of 80 km east and 150 km north of Ship A and is sailing towards the west at 10kmh- 1. A will be at the minimum distance from B in:

Question

Ship A is sailing towards north-east with velocity) overset arrow v=30 hati+50 hatjkmh- 1 where hati points east and hatj, north. The ship B is at a distance of 80 km east and 150 km north of Ship A and is sailing towards the west at 10kmh- 1. A will be at the minimum distance from B in: (A) 4.2 h (B)  3.2 h (C)  2.6 h (D) 2.2 h

Tardigrade Admin · Accepted Answer

vecvr e l = vecv1-v2=40 i+50 j vecrr e l = vecr1- vecr2=-80 i-150 j t min =( vecvr e l ⋅ vecrr e l/ vecvr e l2)=(-3200-7500/√402+5022) t min =(10700/4100)=(107/41)=2.6 h

$4.2 h$

$3.2 h$

$2.6 h$

$2.2 h$

$v_{re l} = v_{1} - v_{2} = 40 i + 50 j$
$r_{re l} = r_{1} - r_{2} = - 80 i - 150 j$
$t_{m i n} = \frac{v _{re l} \cdot r _{re l}}{v _{re l}^{2}} = \frac{- 3200 - 7500}{4 0 ^{2} + 5 0 ^{2} ^{2}}$
$t_{m i n} = \frac{10700}{4100} = \frac{107}{41} = 2.6 h$

Q. Ship A is sailing towards north-east with velocity) v→=30i^+50j^​kmh−1 where i^ points east and j^​, north. The ship B is at a distance of 80km east and 150km north of Ship A and is sailing towards the west at 10kmh−1. A will be at the minimum distance from B in:

4.2h

3.2h

2.6h

2.2h

vrel​=v1​−v2​=40i+50j rrel​=r1​−r2​=−80i−150j tmin​=vrel2​vrel​⋅rrel​​=402+502​2−3200−7500​ tmin​=410010700​=41107​=2.6h

$4.2 h$

$3.2 h$

$2.6 h$

$2.2 h$

$v_{re l} = v_{1} - v_{2} = 40 i + 50 j$
$r_{re l} = r_{1} - r_{2} = - 80 i - 150 j$
$t_{m i n} = \frac{v _{re l} \cdot r _{re l}}{v _{re l}^{2}} = \frac{- 3200 - 7500}{4 0 ^{2} + 5 0 ^{2} ^{2}}$
$t_{m i n} = \frac{10700}{4100} = \frac{107}{41} = 2.6 h$