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A man crosses a river in a boat in minimum time of 10mins with a drift 120m. If he crosses in shortest path he takes 12.5mins. Find (i) width of river (ii) velocity of boat w.r.t water (iii) speed of current.

A man crosses a river in a boat in minimum time of 10mins with a drift 120m. If he crosses in shortest path he takes 12.5mins. Find (i) width of river (ii) velocity of boat w.r.t water (iii) speed of current.

Grade:11

3 Answers

Monil Shah
34 Points
11 years ago

Width of river is 187.5,speed of boat ww.r.t is 0.25 ,velocity of current is 0.2.

 

All speed are in m/ s and distance in m

Arun Kumar IIT Delhi
askIITians Faculty 256 Points
9 years ago
velocity of river=120m/10min=12m/min
now for the man in second case(shortes path
vx^2+vy^2=v^2 where v is magnitude of man's velocity

vy=12m/min since its the shortest path
so vx=root(v^2-12^2)

for the shortest time
d=10*v

10v=12.5*root(v^2-12^2)

v=root(12.5^2*10^2/(12.5^2-10^2))
v=12*12.5/(2.5*22.5)

d=10*v

KAPIL MANDAL
132 Points
9 years ago
Thank you sir for this answer. Thank you very much.

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