Question

A sail boat sails 2 km due East, 5 km 37° South of East and finally an unknown displacement. If
the final displacement of the boat from the starting point is 6 km due East, the third displacement is.​

Answer 1

Answer:

Assume that the sailboat starts from the origin of the Cartesian coordinate system whose positive X axis and positive Y axis are in towards the east and north respectively.

The sailboat initially move 2 km due east.

⇒ The displacement is s1→=2i^.

It then sails 5 km 37o south of east.

⇒ The displacement is s2→=5cos37oi^−5sin37oj^.

Let the subsequent displacement of the sailboat be s3→.

The final position of the sailboat is 6 km due east.

The net displacement is s⃗ =6i^.

s⃗ =s1→+s2→+s3→.

⇒6i^=2i^+5cos37oi^−5sin37oj^+s3→.

⇒s3→=(4−5cos37o)i^+5sin37oj^.

⇒|s3→|=(4−5cos37o)2+(5sin37o)2−−−−−−−−−−−−−−−−−−−−−−√≈3.

⇒θ=arctan(5sin37o4−5cos37o)≈90o.

⇒ The third displacement is approximately 3 km due north.