Multiple choice

As two boats approach the Mumbai, the velocity of boat 1 relative to boat 2 is 10√3 km.hr-1 in a direction of 60° north of east. If boat 2 has a velocity of 15 km.hr-1 due south. What is the velocity of boat 1?

  1. 30 km.hr-1 due north

  2. 5√3 kmhr-1 due east

  3. 10√3 km.hr-1 due north east

  4. 5√3 kmhr-1 due south east

  5. 10√3 km.hr-1 due south east
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let say the velocity of boat 1 with respect to boat 2 is V12 V12 = V1 - V2 It is given that the direction is 60° north of east. Let towards east we have (+i) (unit vector i cap) In north direction we have (+j) (unit vector j cap) So in south we will have (-j) East component of velocity = 10√3 Cos60° = 5√3 North component of velocity = 10√3 Sin60° = 15 Thus V12= 5√3i + 15j (In vector form) V2 = -15j (It is in the south direction that's why it is negative) V12 = V1 - V25√3i + 15j           = V1 - (-15j)5√3i + 15j         = V1 +15j So  V1 = 5√3i (i.e. 5√3 km.hr-1 in the east direction) (Correct Answer)

Keep practicing — related questions