Question

A river flows due south at 5 mi/h. A swimmer attempting to cross the river heads due east swimming at 3 mi/h relative to the water. Find the true velocity of the swimmer as a vector. (Assume that the i vector points east, and the j vector points north.)

Answer 1

Answer:

velocity of swimmer relative to ground = 3 i -5 j

Explanation:

• To cross a river the swimmer swims relative to river in perpendicular direction.

Velocity of river = -5 j (south)

Velocity of swimmer relative to river = 3 i(north)

So

Velocity of swimmer relative to ground = Velocity of swimmer relative to river + Velocity of river

Velocity of swimmer relative to ground = 3 i -5 j

So magnitude of total velocity is $\sqrt{3^2+(-5)^2}$ =$\sqrt{9+25}$ = $\sqrt{34}$

Answer 2

The magnitude of true velocity of the swimmer as a vector is 5.83 mi/h.

Given data:

Velocity of river due south is, $v_{1}=5 \;\rm mi/h$.

Velocity of swimmer due east is, $v_{2}=3 \;\rm mi/h$.

Write the velocities in vector form as,

$v_{net}=3i+(-5j)\\v_{net}=3i-5j$

Negative sign of j is denotes that, south direction is perpendicular to north direction.

Now, true velocity of the swimmer is,

$v_{true}=\sqrt{3^{2}+(-5)^{2}$

$v_{true}=\sqrt{9+25}\\v_{true}=\sqrt{34}\\v_{true}=5.83 \;\rm mi/h$

Thus, we can conclude that the true velocity of the swimmer is 5.83 mi/h.

Learn more about relative velocity here:

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