Question

A bus P is travelling with a speed of 40km/hr towards the north. another bus Q is travelling with a speed of 30km/hr towards east .find magnitude and directions of velocity of bus P with respect to Q and velocity of bus Q with respect to bus P​

Answer 1

Answer:

This is a 2-dimensional problem, and must be done by a careful vector addition.

We start by considering what the motion of X would be relative to Y if bus X were stationary. To Y, bus X would seem to be travelling toward the west at 30 km/hr.

Next, we add the actual speed of bus X, namely 40 km/hr to the north.

These velocity vectors are perpendicular to each other, and so, to add them, we must use Pythagorus' theorem.

v

2

t

=

v

2

X

+

v

2

Y

v

2

t

=

30

2

+

40

2

=

2500

So,

v

t

=

√

2500

=

50

km/hr.

To get the direction of this velocity, we use

tan

−

1

:

θ

=

tan

−

1

(

40

30

)

=

53.1

°

You must be careful in interpreting this direction, however, as the 53.1° angle here would be measured clockwise from the direction of west. We can call this W53.1°N or 53.1° north of west.

As a standard angle (counter-clockwise from east) the angle would be the supplement of this, namely 143.1°.

Explanation:

I am sure you found your answer so please mark as brainlist answer and follow me