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
Answers
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:
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