Question

A man wishes to cross a river of width 120 m by a motorboat. His rowing speed in still water is 5 m/s He takes t seconds to cross point. Speed of water is 3 m/s. Find t​

Answer 1

Answer:

Time to cross the river

(I) t

1

=

3cosθ

120

=

cosθ

40

=40secθ

Drift along the river x=(4−3sinθ)(

cosθ

40

)

=(160secθ−120tanθ)

To reach directly opposite, this drift will be covered by walking speed.

Time taken in this,

(II) t

2

=

1

160secθ−120tanθ

=160secθ−120tanθ

∴ Total time taken

t=t

1

+t

2

=(200secθ−120tanθ)

For t to be minimum,

dθ

dt

=0

or 200secθtanθ−120sec

2

θ=0

or θ=sin

−1

(

5

3

)

t

min

=200secθ−120tanθ (where, sinθ=

5

3

)

=200×

4

5

−120×

4

3

=250−90=160s=2 min 40s=160 s=20×8 s

Answer 2

Answer:

8 seconds

Explanation:

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