Question

A ship is sailing towards north at a speed of $1.25$ m/s. The current is taking it towards east at the rate of $1$ m/s. A sailor is climbing a vertical pole on the ship at the rate of $0.5m/s$. The magnitude of the velocity of the sailor in space is

• A. $2.75$ m/s
• B. $\frac{3\sqrt{5}}{4}$ m/s
• C. $\frac{3\sqrt{5}}{2}$ m/s
• D. None of these

Answer 1

Answer: (B)

$\frac{3\sqrt{5}}{4}$ m/s

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.

$\therefore$ Magnitude of velocity $=\sqrt{1^2+(0.5{)}^2+(1.25{)}^2}$

$=\sqrt{1+0.25+1.5625}=\sqrt{2.8125}$

Now, $2.8125=\frac{45}{16}$

$\Rightarrow$ the answer becomes option $B$