Question

Velocity of boat in still water is (2î +3j)ms!. If it moves in a river flowing with a velocity of
(3î +2j)ms, then the resultant velocity of boat is
[ ]
a) (î+j)ms
b) (3î +3j)ms! c) (2î +2j)ms! d) (5î +5ſ)ms-​

Answer 1

Answer:

The resultant velocity of boat with respect to water is $(-\hat i+\hat j)m/s$.

Explanation:

Given the velocity of boat in still water.

So, it is the velocity of the boat with respect to the still water,

$\vec v_{BG}=(2\hat i+3\hat j)m/s$

Velocity of river means velocity of river with respect to ground,

$\vec v_{RG}=(3\hat i+2\hat j)m/s$

• The velocity of an object with respect to another observer is known as the relative velocity.
• The velocity of a boat relative to the river, $\vec v_{BR}$ is equal to the difference in velocity of the boat relative to the ground, $\vec v_{BG}$ and velocity of river relative to the ground, $\vec v_{RG}$.

       i.e., $\vec v_{BR}=\vec v_{BG}-\vec v_{RG}$

Substituting the given values, the resultant velocity of boat is

$\vec v_{BR}=(2\hat i+3\hat j)-(3\hat i+2\hat j)$

      $=2\hat i+3\hat j-3\hat i-2\hat j=(-\hat i+\hat j)m/s$

Therefore, the resultant velocity of boat with respect to water is $(-\hat i+\hat j)m/s$.

So, the correct answer is option a.

[with - before î].

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Answer 2

Concept:

A moving object's velocity is defined as the rate at which its direction is changing as seen from a particular angle and as measured by a particular unit of time.

Given:

In still water, the velocity of the boat is $(2\hat{i}+3\hat{j})m/s$.

The velocity of river is $(3\hat{i}+2\hat{j})m/s$.

Find:

The resultant velocity of the boat.

Solution:

The velocity of the boat in still water:

$\overrightarrow{v_{B}}=(2\hat{i}+3\hat{j})m/s$

The velocity of river with respect to ground:

$\overrightarrow{v}_{R}=(3\hat{i}+2\hat{j})m/s$

The movement of an object in respect to another observer is known as relative velocity.

The difference between the boat's velocity relative to the ground $\overrightarrow{v}_{B}}$ and the river's velocity relative to the ground $\overrightarrow{v}_{R}}$ determines the velocity of a boat relative to the river $\overrightarrow{v}_{R}}$.

Therefore, $\overrightarrow{v}_{BR}=\overrightarrow{v}_{B}}-\overrightarrow{v}_{R}}$

Now,

$\overrightarrow{v}_{BR}}=(2\hat{i}+3\hat{j})-(3\hat{i}+2\hat{J})\\\overrightarrow{v}_{BR}}=(-\hat{i}+\hat{j})$

The resultant velocity of the boat with respect to water is $(-\hat{i}+\hat{j})m/s$.

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