a person walking at the 3 km per hour find the rain falling vertically when he walks in the opposite direction with the same speed as the rain appears to fall in 45 degree with the vertical what is the speed of the rain and direction of the rain?
THIS IS A QUESTION FROM PLUS TWO PHYSICS MOTION IN A PLANE CHAPTER
Plz help me with a detailed answer .
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Answer:
To man walking a the rate of 3km/h the rain appears to fall vertically
When he increases his speed to
=6km/h it appears to meet him at an angle of 45° with verticl.
Find the velocity the rain.
Solution
Let
i
^
and
j
^
be unit vector in horizontal and vertical respectively
Let, velocity of rain v
r
=a
i
^
+b
j
^
Speed off the rain=
a
2
+b
2
Case 1
When the 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 2
When relative velocity is at 45°
m
=6
i
^
v
rms
=(a−6)
i
^
+b
j
^
=3
i
^
+b
j
^
And since tanθ=
−3
b
tan45°=1
∣b∣=3
Therefore speed=
3
3
+3
2
=3
2
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