Two motor-cyclists set off from points A and B towards each other. The one leaving point A drives uphill with a uniform acceleration a = 2 m/s 2 and an initial velocity v 1 = 72 km/hr, whilst the other goes downhill from point B with an initial velocity v 2 = 36 km/hr and with an acceleration of the same magnitude as the other car. Determine the time of motion and the distance covered by the first motor-cyclist before they meet, if the distance between A and B is S = 300m. Show how the distance between the motor-cyclists will change with time. Plot the change of distance between the motor-cyclists against time. Use the graph to find the moment when the motor-cyclists meet.
Text Solution
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Sol. t = 10s; λ 1 = 100m.
The distance between the motor-cyclists uniformly diminishes with time according to the law
λ = S – t (v 1 + v 2 )
And becomes zero after 10s (fig.)
If the distance from the point where they meet to the point A is l 1 and to the point B is l 2 , then
λ 1 = v 1 t – 
, λ 2 = v 2 t + 
and S = λ 1 + λ 2
so S = v 1 t + v 2 t = t (v 1 + v 2 ).
Hence, t = 
, λ 1 = 
– 
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