# What is the magnitude of the velocity of the boat relative to the shore?A river flows due North at 3.14 m/s. A boat crosses the river from the West shore to the East shore by maintaining a constant...

What is the magnitude of the velocity of the boat relative to the shore?

A river flows due North at 3.14 m/s. A boat crosses the river from the West shore to the East shore by maintaining a constant velocity of 7.2 m/s due East relative to the water.

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### 2 Answers

A river flows due North at 3.14 m/s. A boat crosses the river from the West shore to the East shore and maintains a constant velocity of 7.2 m/s due East relative to the water.

The velocity of the boat relative to the shore is the sum of the velocity of the boat relative to the river and the that of the water relative to the shore. The former is 7.2 m/s due East and the latter is 3.14 m/s due North.

The magnitude of the velocity of the boat relative to the shore is sqrt(3.14^2 + 7.2^2) = 7.854 m/s

The direction at which the boat is moving relative to the shore is at an angle equal to arc tan(3.14/7.2) = 23.56 degrees North of East.

The river flowing due North and the boat is moving due East relative to water, so the boat is moving with the two velocity components.

Component of boat velocity due East = x = 7.2 m/s

Component of boat velocity due North = y = 3.14 m/s

Magnitude of the velocity of boat relative to shore

= square root (x^2 +y^2) = sqare root (7.2^2 + 3.14^2)

= sqare root(61.70) = 7.85 m/s

**Relative velocity of baot relative to shore = 7.85 m/s**