a theif after commuting a theft runs at a uniform speed of 50 ms and after 2 mins a policeman starts running at him with a speed of 60ms with an increasing speed of 5ms .find time taken by the police to catch the theif
Answers
Answer:
According to the question,
Distance between thief and police after 2 minutes = 100 m
Police starts chasing thief with initial speed of 60 and increasing his speed by 5 m every minute.
Let the police chase the thief for t minutes.
Implies, thief covers total 100 + 50t m
Police runs with following pattern 60,65,70...
This is an Arithmetic Progression with a = 60, d = 5 & number of terms = t
t/2(2×60+(t−1)×5)=50t+100
t×(120+5t−5)=100t+200
5t
2
+15t−200=0
t
2
+3t−40=0
t={−3±
(9+160)}/2
=(−3±13)/2=+5
Implies, police will catch thief in 5 minutes.
or the thief is caught after 7 minutes.
Answer:
5 minutes
Step-by-step explanation:
the distance covered by the theif per minute forms an A.P, from after 2 minutes(2×50=100):
the police ran after 2 minutes with initial velocity of 60m/min and and acceleration of . It also forms an ap:
and total distance at time t:
equating both=
as time can't be negative, we take
police will catch the theif after 5min