Question

Velocity of rain is 2 m/s vertically downwards and a man is moving forward with velocity of
1 m/s find angle made umbrella with vertical without dretching himself?

Answer 1

Answer:

dθdt=11+t2.

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. 5.111).

tanθ=atv

Boy should hold his umbrella at an angle θ from the vertical

∴tanθ=atv

To find the rate at which the angle of the axis of umbrella with vertical, we need to find dθ/dt.

dtanθdt=d(atv)dt⇒sec2θdθdt=av

⇒dθdt=avsec2θ=av[1+tan2θ]

=av[1+a2t2v2]=avv2+a2t2

=2×24+4t2=11+t2

⇒dθdt=11+t2.

HOPE IT HELPS U !!

Answer 2

Answer:

hope it's clear for you

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