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Question

Two people leave the same city to different destinations at the same time. Person A leaves due east at a constant speed of 32 kmph and person B leaves due south east at a constant speed of 6 kmph. How fast is the distance between them incresing 4 hours later?

A
122
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B
6
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C
32
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D
24
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Solution

The correct option is C 32
Let O be the starting point

Let x= Distance covered by person A
y= Distance covered by person B
z= Distance between persons A and B
After 4 hours, x=32×4=122 km
y=6×4=24 km
By Cosine Rule: z2=x2+y22xy cos θ(1)
θ=45cos θ=cos 45=12
Value of z after 4 hours
z4 hr=12×12×2+24×242×12×2×24×12
z4 hr=122 km
Let dzdt=z, dxdt=x, dydt=y
Differentiating equation (1) w.r.t time
2zz=2xx+2yy2 cos θ(xy+yx)
122z=122×32+24×612(122×6+24×32)
z=32 Kmph

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