Velocity of train, vT = 30 km /hr
Velocity of car, vc = 40 km/hr
To find: relative velocity of car w.r.t. train. To bring the train at rest, apply equal and opposite velocity of train on car, which is 30 km/hr.
So, relative velocity of car w.r.t train is,
vCT = OD = (OB2 + BD2)1/2
= (402 + 302)1/2
= 50 km/hr
Let <DOB = , then
Relative velocity of one train w.r.to second is,
= 42 - (-30)
= 72 km/hr = 20 m/s
Total distance to be travelled = 120 +80 = 200 m
Time taken, t =
In 10 sec, the two trains will completely cross each other.
Relative velocity of B w.r.to A,
vBA = vB - vA
= 5- 4 = 1 km/hr
Therefore, distance of B ahead of A in time is,
d = vAB x t
= 1 x 3
= 3 km
Here,
Angular frequency, = 600 r.pm
=
We know,
This is the required angular velocity.
Here, we have
Initial velocity, u = 200 cm/s
Acceleration, a = -10 cm/s2
Distance travelled, s = 1500 cm
Time taken, t = ?
Using the relation,
s = ut + 1/2 at2
1500 = 200 t + 1/2(-10)t2
On solving the equation,we get
t = 10 s or t = 30 s
Here, the value of 10 s corresponds to the time when the particle first arrives at the given location. It then crosses this point and at the end of 20 s, its velocity is just 0.
The particle then returns and at the end of 10 s more, is again at the given location from the starting point.