On a cricket field, a rabbit is at the origin ofcoordinate system and a dog at t

Question

On a cricket field, a rabbit is at the origin ofcoordinate system and a dog at the position (46m, 28m). The rabbitruns on the ground with a constant velocity (7.5i + 10j)m/s.The dogcan run with a speed of 5m/s. If the dog starts to run immediatelythe rabbit starts, what is the minimum time in which the dog couldcatch the rabbit? ( ans =4s) On a cricket field, a rabbit is at the origin ofcoordinate system and a dog at the position (46m, 28m). The rabbitruns on the ground with a constant velocity (7.5i + 10j)m/s.The dogcan run with a speed of 5m/s. If the dog starts to run immediatelythe rabbit starts, what is the minimum time in which the dog couldcatch the rabbit? ( ans =4s)

Explanation / Answer

We can write a vector equation frothe dog's displacemntR R= (7.5i + 10j)t - (46i + 28j ) where |R|= |v|t and since |R|2 = (7.5t - 46)2 +(10t -  28j )2 and now |v|2 t2= (7.5t -46)2 + (10t -  28 )2 25t2= 56.25t2 - 690t  +2116+ 100t2 - 560t+ 784 131.25t2 - 1250t + 2900 =0     t2 - 9.52t +22.095 25t2= 56.25t2 - 690t  +2116+ 100t2 - 560t+ 784 131.25t2 - 1250t + 2900 =0     t2 - 9.52t +22.095 Now we have to solve for t t 1,2= [9.52 ± ( 90.7 -88.38)]/2 t 1,2= [9.52 ± 1.52]/2 t1= [9.52 +1.52]/2= 5.52 s t2= [9.52 - 1.52]/2= 3.99 s We select t2= 4 s since minimum timerequired t2= 4 s since minimum timerequired

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