37º and 53º, 12 sec. and 16 sec. x = y 2 /64 –

Sol. Let man swim at angle θ with the line AB than it’s velocity with respect to ground any time t is as shown.

along y-axis

V y = V cos θ = 5 cos θ

So time taken to cross the river t = ....(i)

and velocity along x-axis

V x = u – Vsin θ ⇒ = – 5 sin θ

=

x = – 5t sin θ

For complete motion x = 0

⇒ – 5 t sin θ = 0 ⇒ t = 20 sin θ ....(ii)

by eq (i) and (ii)

100 cos θ sin θ = d = 48 m

sin 2 θ = ⇒ 2 θ = sin –1

2 θ = 74º ⇒ θ = 37º

2 θ = 106º ⇒ θ = 53º

from eq (ii)

for θ = 37º ⇒ t = 12 sec

for θ = 53º ⇒ t = 16 sec

also y-coordinate of man

y = 5t cos θ ....(iii)

x = – y tan θ

by eq (ii) and (iii) x = –