A person P observes that a car is moving with 10 m/s due north and another person Q
observes that same car is moving with 10 m/s due south. Whose observations are correct?
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Answer:
Man 'A' moves in north direction with speed 10 m/s
So we can write
v
a
=0
i
^
+10
j
^
Now for other person
Man 'B' moves in 30 North of East with 10m/s
so we can write
v
b
=10cos30
i
^
+10sin30
j
^
v
b
=5
3
i
^
+5
j
^
Now the relative velocity of B with respect to A is given by
v
ba
=
b
−
a
v
ba
=(5
3
i
^
+5
j
^
)−(0
i
^
+10
j
^
)
v
ba
=5
3
i
^
−5
j
^
Magnitude is given by
∣v
ba
∣=
(5
3
)
2
+(−5)
2
∣v
ba
∣=10 m/s
Therefore the relative velocity of B w.r.t A is 10 m/s
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