To find the magnitude of the resultant of two velocity vectors that are 100 km/hr each and at right angles to each other, we can use the Pythagorean theorem. Here’s the step-by-step solution:
1. Identify the given information:
- Vector 1 (v1) = 100 km/hr
- Vector 2 (v2) = 100 km/hr
- The angle between these two vectors is 90 degrees (right angle).
2. Understand the Pythagorean theorem:
When two vectors are perpendicular to each other, the magnitude of the resultant vector (R) can be found using the Pythagorean theorem:
[tex]\[
R = \sqrt{v1^2 + v2^2}
\][/tex]
3. Substitute the given values into the equation:
[tex]\[
R = \sqrt{100^2 + 100^2}
\][/tex]
4. Calculate the squares of the velocities:
[tex]\[
R = \sqrt{10000 + 10000}
\][/tex]
5. Sum the squared values:
[tex]\[
R = \sqrt{20000}
\][/tex]
6. Find the square root of the sum to get the resultant magnitude:
[tex]\[
R \approx 141.4213562373095 \text{ km/hr}
\][/tex]
Therefore, the magnitude of the resultant vector is approximately 141.42 km/hr.
