Good problem on motion in one dimension

[prathyush.kulkarni]

PLEASE SOLVE THIS WITHOUT USING THE CALCULUS

a man starts walking from a point P. after t seconds another man starts from the same point. they reach the nearer end af a bridge such that the time interval between them is T seconds. the length of the bridge is L meters.
they reach the other end of the bridge simultaneously. assuming that their path is a straight line, they are not accelerating and they walk in the same direction, find the ratio of their speeds.

 

[robphy]

Suggestion: first, draw a position vs time graph of their motion... and label key features using your data. Use this and some knowledge of "the equations of a line" to write down an algebraic expression for the ratio you seek.

 

[quicknote]

I would approach this problem by using the basic principles of motion in one dimension, such as displacement, velocity, and time. I would also use the concept of relative motion, where the motion of one object is considered with respect to another object.

First, let's define our variables:
P = starting point
L = length of the bridge
t = time it takes for the first man to reach the end of the bridge
T = time interval between the two men
v1 = speed of the first man
v2 = speed of the second man

We know that the first man starts walking from point P and reaches the end of the bridge after t seconds. Therefore, his displacement can be calculated as d1 = v1t.

The second man starts walking from the same point P after t seconds. This means that he has already covered a distance of v1t before starting his walk. So, his displacement can be calculated as d2 = v2(T-t).

Since both men reach the end of the bridge simultaneously, their displacements must be equal. Therefore, we can equate d1 and d2 and solve for the ratio of their speeds:

v1t = v2(T-t)
v1/v2 = (T-t)/t

This ratio of speeds will remain the same regardless of the value of t. This is because the men are walking at constant speeds and their paths are straight lines. Therefore, we can choose any arbitrary value for t and still get the same ratio of speeds.

In conclusion, the ratio of their speeds is (T-t)/t. We can also say that the first man is walking (T-t)/t times faster than the second man. This solution does not involve the use of calculus and is based on the fundamental principles of motion in one dimension.