You are developing a machine that automatically cooks and dresses 18 cm long hot

Question

You are developing a machine that automatically cooks and dresses 18 cm long hotdogs for sale. In one part of the machine the hotdogs (in their buns) are moved along a conveyer belt moving at 0.20 m/s. The conveyer carries the dogs in buns under ketchup and mustard dispensers with nozzles positioned 8.0 cm above the hotdog. The dispenser is set to start releasing the condiment when a sensor is tripped by the front of the dog breaking an optical beam on the conveyer. Ideally you want to hotdog covered with the condiment from one end to the other without any falling on the conveyer belt. Where should this sensor be positioned relative to the condiment nozzle and how long should the nozzle remain open before it stops dispensing for a single hot dog?

Explanation / Answer

given,

length of the hot dog = 18 cm

speed of the belt = 0.2 m/s

position of the dispenser = 0 cm above the belt

time it'll take ketchup to reach hot dog = t so,

by second equation of motion

s = ut + 0.5 * at^2

0.08 = 0 + 0.5 * 9.8 * t^2

t = 0.1277 sec

distance covered by the conveyer in 0.1277 sec = 0.2 * 0.1277

distance covered by the conveyer in 0.1277 sec = 0.02554 m

so,

sensor should be positioned 0.02554 m before the dispenser

time it will take hotdog to cover 8 cm = 0.08 / 0.2

time it will take hotdog to cover 8 cm = 0.4 sec

so,

nozzle should remain open for 0.4 sec

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