A train travels east towards Hubli at $80\, km/hr.$ A man on the train runs from the front of the train toward the rear of the train at $10\, km/hr$ with respect to train. As he runs, he carries a plate of fruit with him. He notices a giant spider on the plate and throws the plate away from him (toward the rear of the train) at $20\, km/hr$ with respect to him. Just after that instant, the startled spider jumps towards the man at $5\, km/hr$ with respect to plate. The instant after the spider jumps toward the man, how fast is the spider approaching Hubli?
Given, velocity of train w.r.t. the earth,
$V_{T\to E} =80\, km/h \ldots\left(i\right)$
Velocity of the man w.r.t. the train,
$V_{M\to T}=-10\, km/h \ldots\left(ii\right)$
Velocity of the plate w.r.t. the man,
$V_{P\to M} =- 20\, km/h \ldots\left(iii\right)$
Velocity of the spider w.r.t. the plate,
$V_{S\to P} = 5km/h \dots\left(iv\right)$
From Eqs. (i), (ii), (iii) and (iv), we get
$\therefore$ The velocity of the spider w.r.t. the earth,
$V_{S\to E}=V_{S\to P}+V_{P\to M} +V_{M \to T}+V_{T\to E}$$=5-20-10+80$$= 55km/h$ (towards Hubli)
