Impossible Relative Velocity Values

[Manasan3010]

Homework Statement

Two Aeroplanes fly with velocities 300km/h and 400km/h respectively. What value can't be the relative velocity of one plane respect to other?

Relevant Equations

v=s/t

The answers were
1) 150 km/h
2) 200 km/h
3 )500 km/h
4) 700 km/h
5) 800 km/h (Chosen Solution)

I know that values 700km/h ,100km/h ,-100km/h are possible scenarios but in what ways are 150km/h ,200km/h and 500km/h possible ?

 

[kuruman]

When you add two vectors, what is the possible range of values of the magnitude of the sum?

 

[phyzguy]

The planes can be flying in any directions, for example at an angle to each other.

 

[David Lewis]

The easiest solution is to represent the flight paths with two velocity vectors of magnitude 300 km/hr and 400 km/hr. Then play around with the orientation of the vectors until you find the configuration that yields the smallest and largest possible vector sums. Any answer that falls within that range is correct.