7. To a man moving eastward with a speed of 3 km/h
rain appears to fall vertically downward with a speet
of 4 km/h. Find the actual speed and direction of
rain.
Answers
Answered by
0
Explanation:
Let
i
^
and
j
^
be unit vector in horizontal and vertical respectively.
Let, velocity of rain, v
r
=a
i
^
+b
j
^
Speed of the rain
a
2
+b
2
Case-I
When relative velocity of rain with respect to man is vertical.
V
rms
=
V
r
−
V
m
V
m
=3
i
^
V
rms
=(a−3)
i
^
+b
j
^
Since, V
rms
is vertical
a−3=0⇒a=3
Case II
When relative velocity is at 30°
V
m
=6
i
^
V
rms
=(a−6)
i
^
+b
j
^
=3
i
^
+b
j
^
Since, tanθ=
−3
b
tan30°=
−3
b
b=
3
1
×(−3)
b=−
3
∣b∣=
3
The therefore, speed:-
=
3
2
+(
3
)
2
=
(9+3)
=
12
=
4×3
=2
3
Answered By
Divyanshu
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