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#141 Sam’s speed

Sam checked on his satnav and decided he could leave at 2pm for the 20-kilometre journey to the dentist. His appointment was at 2.30 (tooth hurty, boom-tish!). However, traffic that day was as sticky as the toffees his dentist had told him not to eat, and Sam spent the first 10 kilometres doing 30 kilometres per hour in a steady stream of traffic. Luckily, at the 10-kilometre mark, the road ahead miraculously cleared. What speed should Sam now maintain to arrive at his appointment on time?

Solution next week

#140 Drum roll

Solution

Mr Hasty is half right. At any instant in time, the contact point of the drum with the ground is stationary, with the drum rotating about this point. The top of the drum, which is in contact with the plank, therefore moves at twice the speed of the centre, or axis, of the drum. So, for every metre Mr Bodger walks towards the drum, it advances half a metre. To reach the edge of the drum, which is initially 4.5 metres away, he must therefore walk 9 metres.