Question

A ship is sailing towards north at a speed of
√2 m/s. The current is taking it towards East
at the rate of 1 m/s and a sailor is climbing a vertical pole on the ship at the rate of 1 m/s.
Find the velocity of the sailor in space.​

Answer 1

Answer:

If seen the state of man as described above in a cartesian co-ordinate system, we see that the speeds of the man are in three perpendicular directions and thus their resultant will be the square root of the sum of squares of each.

∴ Magnitude of velocity =

1

2

+(0.5)

2

+(1.25)

2

=

1+0.25+1.5625

=

2.8125

Now, 2.8125=

16

45

⇒ the answer becomes option B

Answer 2

If seen the state of man as described above in a cartesian co-ordinate system, we see that the speeds of the man are in three perpendicular directions and thus their resultant will be the square root of the sum of squares of each.

∴ Magnitude of velocity:

$\sqrt{ {1}^{2} {(0.5)}^{2} {(1.25)}^{2} } \\ \\ = \sqrt{1 + 0.25 + 1.5625} \\ \\ = \sqrt{2.8125}$

As 2.8125 = 45/16

Then;

$\sqrt{ \frac{45}{16} } \\ \\ = \sqrt{ \frac{3 \times 3 \times 3 \times 5}{4 \times 4 } } \\ \\ \ \ \ \boxed{\boxed{\boxed{\frac{3\sqrt{5} }{4} }}}$

I HOPE IT HELPS.