Question

A train travels east towards Hubli at $80km/hr.$ A man on the train runs from the front of the train toward the rear of the train at $10km/hr$ 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 $20km/hr$ with respect to him. Just after that instant, the startled spider jumps towards the man at $5km/hr$ with respect to plate. The instant after the spider jumps toward the man, how fast is the spider approaching Hubli?

• A. 45km/hr
• B. 115 km/hr
• C. 55 km/hr
• D. 95 km/hr

Answer 1

Answer: (C)

Given, velocity of train w.r.t. the earth,

$V_{T\to E}=80km/h\dots \left(i\right)$
Velocity of the man w.r.t. the train,
$V_{M\to T}=-10km/h\dots \left(ii\right)$
Velocity of the plate w.r.t. the man,
$V_{P\to M}=-20km/h\dots \left(iii\right)$
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)