Question

A boat moves perpendicular to the bank with
a velocity of 7.2 km/h. The current carries it
150 m downstream, find the velocity of the
current. (The width of the river is 0.5 km).
1) 0.4ms-1
2) 1.2ms-1
3) 0.5ms-1
4) 0.6ms-1

Answer 1

Answer:

option 4

Explanation:

Width of river d=0.5 km

Velocity of boat perpendicular to the river current v=7.2 km/h

So,, time taken to cross the river t=

v

d

=

7.2

0.5

hr=

7.2

0.5

×3600=250 s

Drift of the boat x=150 m

So, velocity of current V

R

=

t

x

=

250

150

=0.6 m/s

Answer 2

Answer:

$\boxed{\mathfrak{(4) \ 0.6 ms^{-1}}}$

Explanation:

$\rm V_{boat} = 7.2 \ km/h \\ \rm = 7.2 \times \dfrac{5}{18} \ m/s \\ \rm = 2 \ m/s$

Width of the river (d) = 0.5 km = 500 m

Time to reach other side (t):

$\rm \implies t = \dfrac{d}{V_{boat}} \\ \\ \rm \implies t = \dfrac{500}{2} \\ \\ \rm \implies t =250 \: m {s}^{ - 1}$

Horizontal distance travelled by due to current (AB) = 150 m

So,

$\rm \implies 150 = V_{river} \times 250 \\ \\ \rm \implies V_{river} = \dfrac{150}{250} \\ \\ \rm \implies V_{river} = 0.6 \: m {s}^{ - 1}$

$\therefore$ Velocity of current ($\sf V_{river}$) = 0.6 m/s