Chapter 5, Problem 94A

To determine

To identify: The greater component of velocity, x or y.

Answer to Problem 94A

The greater component of velocity is y-component.

Explanation of Solution

Given:

Velocity of car is 50 km/hr in a direction of $60°$ north of east.

Formula used:

The x-component and y-component of any vector R that is inclined at an angle $\theta$ with the horizontal are,

  $\begin{array}{l}{R}_x=R\cos \theta \\ R_y=R\sin \theta \end{array}$

Calculation:

Velocity is given 50 km/hr in a direction of $60°$ north of east.

Graphically it can be represented as,

  

x-component of velocity is,

  $\begin{array}{c}{v}_x=v\cos 60°\\ =50\cos 60°\\ =50\times 0.5\\ =25\text{ km/hr}\end{array}$

y-component of velocity is,

  $\begin{array}{c}{v}_y=v\sin 60°\\ =50\sin 60°\\ =50\times 0.866\\ =43.30\text{ km/hr}\end{array}$

Conclusion:

Therefore, it is observed that the value ofy-component of velocity is larger.