3.4 Resultant motion  (Page 2/3)

Problem 1 : An aircraft flies with a wind velocity of 200 km/hr blowing from south. If the relative velocity of aircraft with respect to wind is 1000 km/hr, then find the direction in which aircraft should fly such that it reaches a destination in north – east direction.

What does this relative velocity of aircraft with respect to wind mean? Is it the resultant velocity of the aircraft or is it the velocity of aircraft in still air?

Problem 2 A girl, starting from a point “P”, wants to reach a point “Q” on the opposite side of the bank of a river. The line PQ forms an angle 45° with the stream direction. If the velocity of the stream be “u”, then at what minimum speed relative to stream should the girl swim and what should be her direction?

What does this relative speed of girl with respect to stream mean? Is it the resultant speed of the girl or is it the speed of girl in still water?

In this module, we shall learn to know the meaning of each term exactly. As a matter of fact, the most critical aspect of understanding motion in a medium is to develop skill to assign appropriate velocities to different entities.

Relative velocity with respect to a medium

We consider here an example, involving uniform motion of a person in a train, which is itself moving with constant velocity. Let us consider that the person moves across (perpendicular) the length of the compartment with constant speed “v”.

Uniform motion of the person is viewed differently by the observers on ground and on the train. Let us first think about his motion across the width of the train, when the train is not moving.

The observers in two positions find that the motion of the person is exactly alike. In the figure, we have shown his path across the floor of the train (“B”). Evidently, the path of the motion of the person is a straight line for both observers attached to ground ("O") and train ("B").

Now let us consider that the train moves with a speed “u” to the right. Now, situation for the observer on thetrain has not changed a bit. The observer still finds that the speed of the person walking across the floor is still “v” and thepath of motion is a straight line across the compartment. With our experience, we can imagine other persons walking on a train. Does the motion of co-passengers is different than what we see their motion on the ground? Our biological capacity to move remains same as on the ground. It does not matter whether we are walking on the ground or train.

The motion of the person, however, has changed for the observer on the ground. By the time the person puts hisnext step on the floor in the y-direction, the train has moved in the x-direction. The position of the person after completing thestep, thus, shifts right for the observer on the ground. Since, the velocities of person and train are uniform, the observer on theground finds that the person is moving along a straight path making certain angle with the y-direction.