Question

Two trains depart from one station, one going north at $30.0$ miles per hour, and another going northeast (${45}^o$ north of east) at $60.0$ miles per hour.
At what rate does the distance between the two trains increase, in miles per hour?

• A. $12.4mph$
• B. $30.0mph$
• C. $40.0mph$
• D. $42.4mph$
• E. $44.2mph$

Answer 1

The correct option is A $12.4mph$

As one train is going towards northeast the component of its velocity in north direction will be ,

$v_{n2}=60\cos 45=60\times 1/\sqrt{2}$ ,

given that $v_{n1}=30.0mph$ is the velocity of train going toward north,

now two trains have velocities in same direction (north) , therefore relative velocity of the trains $v=v_{n2}-v_{n1}=42.4-30.0$

or $v=12.4mph$ ,

that is the rate with which the distance between the two trains increase .