Starting from a place, two person travel in bicycles along two perpendicular roads at speed of u km/hr and v km/hr. What is the distance between their positions after t hours?
Does this problem use Pythagoras theorem? Do we also need to use Time-Distance-Speed formula? How do we connect this formula with Pythagoras theorem and solve the problem?
Does this problem use Pythagoras theorem? Do we also need to use Time-Distance-Speed formula? How do we connect this formula with Pythagoras theorem and solve the problem?
2 Answers
Use the definition of velocity (the time-distance-speed formula) to determine how far each went, then Pythagorus.
Explanation:
First, we calculate the distance each has travelled. Using
The rider travelling at
The rider travelling at
Since they are travelling along perpendicular directions, we must use Pythagorus' theorem to find the distance between them:
Finally, we take the square root of this equation, and simplify a bit:
which we can also write as
Explanation:
Let person 'x' starts from O and reached at A in t hours and at the same hours another person stars from O and reached Y.
First we have calculate distance between OA and OB. After that we have to calculate distance between AB.
We know, distance = speed x time.
For first person i.e. x speed is u km/hr and time is t hr.
so, distance (OA) = u km/hr x t hr = ut kms.
For second person, speed is v km/hr and time is t hr
So distance (OB) = v km/hr x t hr = vt kms.
Now, AOB has formed a right angle triangle whose height is OA and base is OB. We have to find the hypotenuse i.e. AB.
As per Pythagoras theory,
Hypotenuse =
Or, AB =
Or, AB =
Or, AB =
Or, AB =
Or, AB =
Hence the distance AB =