One of the rectangular components of a velocity of 20 `ms^(-1)` is 10 `ms^(-1)`. Find the other component.

Options

A. `10sqrt(3) ms^(-1)`
B. `20 sqrt(3) ms^(-1)`
C. `5sqrt(3) ms^(-1)`
D. `35sqrt(3) ms^(-1)`

Answer

To solve the problem, we need to find the other rectangular component of the velocity given one component and the total magnitude of the velocity. Let's break it down step by step.

### Step 1: Understand the given information
We know:
- The total velocity \( V \) is \( 20 \, \text{ms}^{-1} \).
- One component of the velocity \( V_x \) is \( 10 \, \text{ms}^{-1} \).

### Step 2: Use the Pythagorean theorem for vector components
The magnitude of the velocity vector can be expressed using the Pythagorean theorem:
\[ V = \sqrt{V_x^2 + V_y^2} \]
where \( V_y \) is the other component we need to find.

### Step 3: Substitute the known values into the equation
Substituting the known values into the equation:
\[ 20 = \sqrt{10^2 + V_y^2} \]

### Step 4: Square both sides to eliminate the square root
Squaring both sides gives:
\[ 20^2 = 10^2 + V_y^2 \]
\[ 400 = 100 + V_y^2 \]

### Step 5: Solve for \( V_y^2 \)
Rearranging the equation to solve for \( V_y^2 \):
\[ V_y^2 = 400 - 100 \]
\[ V_y^2 = 300 \]

### Step 6: Find \( V_y \) by taking the square root
Taking the square root of both sides gives:
\[ V_y = \sqrt{300} \]
This can be simplified as:
\[ V_y = \sqrt{100 \times 3} = 10\sqrt{3} \, \text{ms}^{-1} \]

### Conclusion
The other component of the velocity is:
\[ V_y = 10\sqrt{3} \, \text{ms}^{-1} \]