A river flows due east. A boat travels with constant speed due North across the

Question

A river flows due east. A boat travels with constant speed due North across the river from point A to point B. The speed of the boat relative to the water is 5 m/s. The river is 21 m wide and it takes the boat 7 seconds to travel from A to B. What is the speed of the current of the river (the speed of the water relative to the earth)?

(6 pts) 5. A river flows due east. A boat travels with constant speed due north across the river from point A to point B. The speed of the boat relative to the water is 5.00 m/s. The river is 21.0 m wide and it takes the boat 7.00 s to travel from A to B. What is the speed of the current in the river (the speed of the water relative to the earth)? (a) 8.00 m/s (b) 5.83 m/s (c) 4.00 m/s (d) 2.00 m/s (e) none of the above

Explanation / Answer

Using relative motion

Speed of boat w.r.t ground = Speed of boat w.r.t current + Speed of current w.r.t ground

Vbg = Vbc + Vcg

We need Vcg = ?

Given that

Vbg = 5 m/sec

We know that

Speed = distance/time taken

Vbc = 21 m/7 sec = 3 m/sec due north

Vbc = 3 j

Now given that river is flowing due east, So

Vcg = Vcg i

So now

Vbg = Vbc + Vcg

Vbg = 3 j + Vcg i

Now Magnitude of Vbg will be

|Vbg| = sqrt (3^2 + Vcg^2)

Since given that |Vbg| = 5 m/sec

5 = sqrt (9 + Vcg)

9 + Vcg^2 = 25

Vcg^2 = 16

Vcg = sqrt 16 = 4 m/sec

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