Question

What are the speeds of two objects if they move uniformly towards each other, they get 4m closer in each second and if they move uniformly in the same direction with the original speeds they get 4m closer in each 10 sec ?

• A. 2.8 m/s and 1.2 m/s
• B. 5.2 m/s and 4.6 m/s
• C. 3.2 m/s and 2.1 m/s
• D. 2.2 m/s and 1.8 m/s

Answer 1

The correct option is D 2.2 m/s and 1.8 m/s

Case I: (Moving towards each other)

Relative velocity

$v_1+v_2=\frac{Distance}{time}$

$v_1+v_2=\frac{4m}{1s}$

$v_1+v_2=4㎧⟶1$

Case II: Moving in same direction

Relative velocity

$v_1-v_2=\frac{Distance}{time}$

$v_1-v_2=\frac{4m}{10s}$

$v_1-v_2=0.4㎧⟶2$

Adding $1$ and $2$

$2v_1=4.4$

$\therefore v_1=2.2㎧$

Putting this value in equation $2$

$v_2=4-v_1$

$=4-2.2$

$v_2=1.8㎧$