A child runs at speed vc while an adult runs at speed va. If the adult gives the child a head start of distance d, how long will it take for the adult to catch the child? Express your answer in terms of va and vc and d.
Answers
A child runs at speed vc while an adult runs at speed va. If the adult gives the child a head start of distance d, how long will it take for the adult to catch the child? Express your answer in terms of va and vc and d.
Concept:
The relative velocity of an object is the speed of the thing as measured by another observer. It is the rate at which, over time, the relative locations of two objects change with respect to one another.
Mathematically expressed as- Relative Velocity = distance/ time
Given:
Speed of child = vc
Speed of adult = va
head start for the child = d
Find:
We need to determine the time taken by the adult to catch the child
Solution:
When an item is moving, its velocity is the rate at which its direction is changing as seen from a certain point of view and as measured by a specific unit of time.
While the velocity of an object in relation to another observer is known as its relative velocity. It is the pace at which one object's relative location changes in relation to another object over time.
Here, it has been understood that the relative velocity of adult w.r.t child is given as- (va - vc)
while the head start for the child was given as d
We know, velocity is mathematically expressed as- Relative Velocity = distance/ time
Therefore, time = distance / relative velocity
time = d / va - vc
Thus, the time taken by the adult to catch the child is d / va - vc.
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