Question I would like to know AMD how calculated

Question

Maureen is riding a boat which can travel with a speed of 13 m/sec in still water.
There was her friend Krishna 68metre distant from her at downstream is drowning.
By how much time Maureen will rescue krishna If the speed of the stream is 4 m/sec.

Assumption: Krishna is not offering any resistance to water.
He is going along stream.

Answer 1

v = speed of boat in still water = 13 m/s

x₀ = initial distance from boat to Krishna =  68 m

u = stream speed = 4 m/s

w = Krishna's speed = u = 4 m/s (Krishna is drifting with the stream)

 

If the boat goes downstream toward Krishna, its total speed is v + u, while Krishna drifts downstream at speed w = u.

 

t = intercept time

 

The positions of the boat and Krishna must match at time t.  Set the 2 positions equal using distance = speed x time, and solve for time.

 

The boat travels a distance (v + u)t, while Krishna drifts a distance wt = ut, starting from x₀.

 

(v + u)t = x₀ + ut

 

The x₀ accounts for Krishna's "head start."

 

(v + u)t = x₀ + ut

 

vt + ut = x₀ + ut

 

vt = x₀

 

t = x₀/v = (68 m) / (13 m/s) ≅ 5.23 s

 

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