When two bodies move uniformly towards each other, the distance betwee

1.	When two bodies move uniformly towards each other, the distance between them diminishes by 16 m every 10s. If the bodies move with vlocitics of the same magnitude and in the same direction as before, the distance between them will increase by 3m every 5s. What is velocity of each body?
Answer» Let v_A and v_Bbe the velocities of the two bodies A and B. When two bodies are moving towards each other: Relative velocity of body A w.r.t.B. v = v_A -(-v_B) = v_A + v_B Since, distance diminishes by m. every 10 s. v = 16/10 = 1.6 ms^-1. or, v_A + v_B = 1.6 .....(i) When two bodies move in the same direction: Relative velocity of body A w.r.t.B. v = v_A - v_B. Since, distance increase by 3m every 5s, v' = 3/5 = 0.6 ms^-1 or, v_A - v_B = 0.6......(ii) On solving the equations (i) and (ii), we get v_A = 1.1 ms^-1 and v_B = 0.5 ms^-1.

When two bodies move uniformly towards each other, the distance between them diminishes by 16 m every 10s. If the bodies move with vlocitics of the same magnitude and in the same direction as before, the distance between them will increase by 3m every 5s. What is velocity of each body?

Answer»

Let v_A and v_Bbe the velocities of the two bodies A and B.

When two bodies are moving towards each other: Relative velocity of body A w.r.t.B.

v = v_A -(-v_B) = v_A + v_B

Since, distance diminishes by m. every 10 s.

v = 16/10 = 1.6 ms^-1.

or, v_A + v_B = 1.6 .....(i)

When two bodies move in the same direction: Relative velocity of body A w.r.t.B.

v = v_A - v_B.

Since, distance increase by 3m every 5s,

v' = 3/5 = 0.6 ms^-1

or, v_A - v_B = 0.6......(ii)

On solving the equations (i) and (ii), we get

v_A = 1.1 ms^-1 and v_B = 0.5 ms^-1.