While we walk in rain, the umbrella is held along the line of a)our velocity b) velocity of rain c) relative velocity of rain with respect to us d) none of these
Answers
Answer:
Our Velocity
Explanation:
Velocity of rain
v
→
rain.boy
=
v
→
rain
−
v
→
boy
=
v
→
rain
+(−
v
→
boy
)
At any time t, rain will appear to the boy as shown in Fig.
tanθ=
v
at
Boy should hold his umbrella at an angle θ from the vertical
∴tanθ=
v
at
To find the rate at which the angle of the axis of umbrella with vertical, we need to find dθ/dt.
dt
dtanθ
=
dt
d(
v
at
)
⇒sec
2
θ
dt
dθ
=
v
a
⇒
dt
dθ
=
vsec
2
θ
a
=
v[1+tan
2
θ]
a
=
v[1+
v
2
a
2
t
2
]
a
=
v
2
+a
2
t
2
av
=
4+4t
2
2×2
=
1+t
2
1
⇒
dt
dθ
=
1+t
2
1
Explanation:
Velocity of rain with respect to boy
v
→
rain.boy
=
v
→
rain
−
v
→
boy
=
v
→
rain
+(−
v
→
boy
)
At any time t, rain will appear to the boy as shown in Fig.
tanθ=
v
at
Boy should hold his umbrella at an angle θ from the vertical
∴tanθ=
v
at
To find the rate at which the angle of the axis of umbrella with vertical, we need to find dθ/dt.
dt
dtanθ
=
dt
d(
v
at
)
⇒sec
2
θ
dt
dθ
=
v
a
⇒
dt
dθ
=
vsec
2
θ
a
=
v[1+tan
2
θ]
a
=
v[1+
v
2
a
2
t
2
]
a
=
v
2
+a
2
t
2
av
=
4+4t
2
2×2
=
1+t
2
1
⇒
dt
dθ
=
1+t
2
1