Chapter 5, Problem 19A

For Questions 18—19, recall that when two vectors in the same or exactly opposite directions are added, the magnitude of their resultant is the sum or difference of their original magnitudes.

Calculate the magnitude of the resultant of a pair of 100-km/h velocity vectors that are at right angles to each other.

To determine

Magnitude of resultant velocity.

Answer to Problem 19A

Resultant velocity is, $v_r=141.42\text{ km/h}$

Explanation of Solution

Given :

A pair of velocity of 100 km/h which are right angle with each other.

Formula used :

  $R=\sqrt{A^2+B^2}$

Where, R is resultant vector, A and B are two vectors which are perpendicular to each other.

Calculation :

Pair of velocity is represented by below figure.

  

Here, both velocity are perpendicular to each other.

Therefore, their resultant velocity will be,

  $v_r=\sqrt{v^2+v^2}$

Now, substituting the value of v and solve.

  $\begin{array}{l}{v}_r=\sqrt{{100}^2+{100}^2}\\ =\sqrt{20000}\\ =141.42\text{ km/h}\end{array}$

Conclusion :

Therefore, resultant velocity will be equal to 141.42 km/h