Two perpendicular forces of magnitudes 10 N and 5 N act at a point. Find their resultant.

Answer

To find the resultant of two perpendicular forces of magnitudes 10 N and 5 N, we can follow these steps:

### Step 1: Identify the Forces
Let the first force \( A = 10 \, \text{N} \) and the second force \( B = 5 \, \text{N} \). The angle between the two forces is \( 90^\circ \).

### Step 2: Use the Resultant Force Formula
The formula for the resultant \( R \) of two forces acting at an angle \( \theta \) is given by:
\[ R = \sqrt{A^2 + B^2 + 2AB \cos \theta} \]
Since the forces are perpendicular, \( \theta = 90^\circ \), and we know that \( \cos 90^\circ = 0 \).

### Step 3: Substitute the Values
Substituting the values into the formula:
\[ R = \sqrt{10^2 + 5^2 + 2 \cdot 10 \cdot 5 \cdot \cos 90^\circ} \]
This simplifies to:
\[ R = \sqrt{10^2 + 5^2} \]
Calculating \( 10^2 \) and \( 5^2 \):
\[ R = \sqrt{100 + 25} \]

### Step 4: Calculate the Resultant
Now, we can calculate:
\[ R = \sqrt{125} \]
To find the square root:
\[ R = 11.18 \, \text{N} \, (\text{approximately}) \]

### Final Result
Thus, the resultant of the two perpendicular forces is approximately \( 11.18 \, \text{N} \).

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