A man starts running from point p at 11:00
a.M. With a speed of 10 km/hr. He runs for 2 hours and then takes a 1 hour rest. He continues this till he is caught by another man who starts at 2:00 p.M. From point p and runs non-stop at a speed of 15 km/hr towards the first man. At what time (in p.M.) will the first man be caught?
Answers
Answer:
4 : 40 PM
Explanation:
A man starts running from point p at 11:00 a.M. With a speed of 10 km/hr. He runs for 2 hours and then takes a 1 hour rest. He continues this till he is caught by another man who starts at 2:00 p.M. From point p and runs non-stop at a speed of 15 km/hr towards the first man. At what time (in p.M.) will the first man be caught?
Let say after 3T hrs from 11:AM man was Caught
T should be an ineteger
Speed = 10 km/Hr
Distance Covered = 10 *(3T - T) = 10*2T = 20T
Man b started after 3 hrs
Speed = 15 km/hr
Distance covered = 15*(3T-3) = 45T - 45
20T = 45T - 45
=> 25T = 45
=> T < 2
Distance covered by a in 3 hrs = 20 km
Distance by a from 5 hrs to 6 hrs = 40 km
Time Taken by b to reach 40 km = 40/15 = 2 hr 40 mins
First Man be caught at 4 : 40 PM
◆ Answer -
(d) |AB| = 8.5 m
● Explaination -
Let i, j & k be unit vectors along X-axis, Y-axis & Z-axis.
A = i + 2j - 3k
B = 3i + 4j + 5k
Displacement of the man is calculated by -
AB = B - A
AB = (3i + 4j + 5k) - ( i + 2j - 3k)
AB = 2i + 2j + 8k
Magnitude of displacement is calculated by -
|AB| = √(2² + 2² + 8²)
|AB| = √(4 + 4 + 64)
|AB| = √(72)
|AB| = 2√18
|AB| = 8.48 m
From the options, 8.5 m is the most appropriate.