A man running on a horizontal surface at 3 m/s hids falling rain naturally at 4m/s .find the actual velocity of the rain drops
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let consider the velocity of rain,
v
r
=a
i
^
+b
j
^
v
m
= velocity of man
v
rm
= velocity of rain with respect to man
Condition (1):
v
m
=8
i
^
v
rm
=0
i
^
+b
j
^
v
r
−
v
m
=b
j
^
a
i
^
+b
j
^
−8
i
^
=b
j
^
(a−8)
i
^
+b
j
^
=b
j
^
a−8=0
a=8
Condition (2):
v
m
=12
i
^
v
rm
=
v
r
−
v
m
v
rm
=(a
j
^
+b
j
^
)−12
i
^
v
rm
=(a−12)
i
^
+b
j
^
Make 30
0
angle to the vertical,
a−12
b
=tan30
0
4−12
b
=
3
1
b=−
3
4
So, velocity of rain with respect to the road is,
v
r
=8
i
^
−
3
4
j
^
It's magnitude, ∣
v
r
∣=
(8)
2
+(−
3
4
)
2
v
r
=8.32m/s
Explanation:
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