Question

An observer on ground sees a boat cross a river of width 800m perpendicular to it's stream in 200 seconds . He also finds a man on the raft floating at speed of 3m/s with river. The distance travelled by boat as seen by man on the raft in crossing the river is ?

Answer 1

Net speed of the boat with respect to ground is perpendicular to river current

it is given by

$speed = \frac{distance}{time}$

here

distance = 800 m

time = 200 s

$speed = \frac{800}{200} = 4m/s$

now if the man on the raft is observing the same boat then he will see the boat moving with respect to river.

now we can say

$\vec v_{br} + \vec v_r = \vec v_{net}$

here we can say that since net velocity is perpendicular to river flow

so we can use Pythagoras theorem to find the relative speed

$v_{net}^2 + v_r^2 = v_{br}^2$

$4^2 + 3^2 = v_{br}^2$

$v_{br} = 5 m/s$

now distance covered with respect to river in same time is given by

$d = relative \. speed * time$

$d = 5*200 = 1000 meter$

So the man in the raft will see a total distance of 1000 m with respect to himself