Numerical Problems Based on Relative Velocity of Two Inclined Motions for Class 11 Physics

Let East be the positive x-axis ($\hat{i}$) and North be the positive y-axis ($\hat{j}$).

Velocity of the train ($\vec{v}_T$) $= 30\hat{i}$

Velocity of the car ($\vec{v}_C$) $= 40\hat{j}$

Velocity of the car relative to the train ($\vec{v}_{CT}$) is:

Magnitude:

Direction: Let $\theta$ be the angle made with the North direction (y-axis).

Since the x-component is negative (West) and the y-component is positive (North), the direction is $36^\circ 52’$ West of North.

Let East be $+\hat{i}$ and upward be $+\hat{j}$. Therefore, West is $-\hat{i}$ and downward is $-\hat{j}$.

Velocity of rain ($\vec{v}_R$) $= -35\hat{j}$

Velocity of the woman ($\vec{v}_W$) $= -12\hat{i}$ (since she is riding East to West)

The relative velocity of rain with respect to the woman ($\vec{v}_{RW}$) determines the apparent direction of the rain.

The rain appears to be coming from the front (West) and falling downwards. She must point her umbrella in the direction the rain is coming from.

Let $\theta$ be the angle the umbrella makes with the vertical:

She should hold the umbrella at an angle of $19^\circ$ with the vertical towards the West.

Let East be $+\hat{i}$ and upward be $+\hat{j}$.

Velocity of the person ($\vec{v}_P$) $= 4.8\hat{i}$

Velocity of rain relative to person ($\vec{v}_{RP}$) $= -6.4\hat{j}$ (vertically downwards)

We know that $\vec{v}_{RP} = \vec{v}_R – \vec{v}_P$, so the actual velocity of the rain ($\vec{v}_R$) is:

Actual Speed:

Direction: Let $\theta$ be the angle with the horizontal.

Let East be $+\hat{i}$ and North be $+\hat{j}$.

Velocity of the ship relative to the sea ($\vec{v}_S$) $= 12\hat{i}$

Velocity of the woman relative to the ship ($\vec{v}_{WS}$) $= 5\hat{j}$

The actual velocity of the woman relative to the sea ($\vec{v}_W$) is the vector sum:

Magnitude:

Direction: Let $\theta$ be the angle North of East.

Let East be $+\hat{i}$ and North be $+\hat{j}$. (South is $-\hat{j}$)

Velocity of the plane relative to the air ($\vec{v}_{PA}$) $= 500\hat{i}$

Velocity of the wind relative to the ground ($\vec{v}_A$) $= -90\hat{j}$

The actual velocity of the plane relative to the ground ($\vec{v}_P$) is:

Speed (Magnitude):

Direction: Let $\theta$ be the angle South of East.