Chapter 5, Problem 9STP

To determine

The net distance from car to the present position of man.

Answer to Problem 9STP

The net distance from car to the present position of man is $\text{546}\text{.44 m}$.

Explanation of Solution

Given:

A man stands initially 310 m north from his car and now moves westwards with a constant velocity of 10 km/hr for 2.7 min.

Formula Used:

For two given vectors A and B and their resultant R, the Pythagoras theorem is expressed as,

  $\text{R}=\sqrt{{\text{A}}^2+{\text{B}}^2}$

The total distance travelled in time t with a speed v is

  $D=t\times v$

Calculation:

Here the distance travelled by the man from his car can be represented as vectors such that they are perpendicular to each other. The two distance vectors have been given and the resultant displacement has to be calculated.

Thus, Pythagoras theorem can be applied to evaluate the unknown distance.

The distance walked by the man from his car is shown in vector form in Figure 1.

  

Here, the distance travelled in west direction can be calculated from the velocity and time as,

  $\text{D}=v\times t$

The velocity of the man is given as 10 km/hr and the time taken to travel is 2.7 minutes. Firstly, the time in hours has to be calculated, which is,

  $\begin{array}{c}{t}_h=\frac{2.7}{60}\\ =0.045\text{ hours}\end{array}$

Now, the distance travelled in west direction is obtained as,

  $\begin{array}{c}\text{D}=10\times 0.045\\ =0.45\text{ km}\\ =\text{450 m}\end{array}$

Applying the Pythagoras theorem for the given vectors, the distance between the car and the current position of the man is obtained as ,

  $\begin{array}{c}\text{x}=\sqrt{{310}^2+{450}^2}\\ =546.44\text{ m}\end{array}$

Conclusion:

The net distance from car to the present position of the man 546.44 m.