Question

a body travels a distance of 15 m from a to b and then moves a distance of 20 metre at right angle to ab what is the total distance and displacement ​

Answer 1

Answer:

Distance is total length of path travelled, i.e. AB+AC= 15+20= 35 mtrs. Answer: The displacement is total distance between final point and initial point

Explanation:

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Answer 2

Answer :-

Given :-

A body travels a distance of 15 meters from a to b .

Similarly,

Then the body moved a distance of 20 meters at right angled to ab .

Required to find :-

• Total distance ?
• Total displacement ?

Condition used :-

Distance is the actual distance between any two points .

Displacement is the shortest distance between any two points .

Pythagorean theorem states that,

$\red{\boxed{\mathrm{{(perpendicular)}^{2} + {(Base)}^{2} = {(hypotenuse)}^{2}}}}$

Solution :-

It is given that,

A body travels a distance of 15 meters from a to b .

Similarly,

The body moved a distance of 20 meters at right angled to ab .

So,

From the above two lines we can conclude that ,

The body moved in a right angled path .

So,

Here, if we draw a diagram on the given information we will be left with a right angled triangle .

So, using the properties of the right angled triangle we can find the required angle .

Here we assume that the body had stopped at a point c after moving a distance of 20 meters at right angled to ab .

( Refer to the attachment for the diagram )

Since we know that,

Distance is the actual path between any two points .

So,

According to figure ,

The actual path is AC .

But , at first the body travelled a distance of 15 meters from a to b

Secondly, the body travelled a distance of 20 meters at right angled to ab which is taken as the point c .

So,

Distance = ab + bc

Distance = 15 meters + 20 meters

Distance = 35 meters

Hence,

$\large{\boxed{\tt{ Total \; distance = 35 \; meters }}}$

Similarly,

We also known that,

Displacement is the shortest path between any two possible .

So, in this case

we can consider the length of the hypotenuse of the right angled triangle as the length of the displacement .

So,

Using Pythagorean theorem ,

Let's find the length of the diagonal .

$\tt{{(perpendicular)}^{2} + {(Base)}^{2} = {(Hypotenuse)}^{2}}$

This implies ,

$\rm{ ( hyp.{)}^{2} = {(15)}^{2} + {(20)}^{2}}$

$\rm{ {(hyp.)}^{2} = 225 + 400 }$

$\rm{ {(hyp.)}^{2} = 625 }$

$\rm{ hyp. = \sqrt{625}}$

$\rm{ ac = 25 meters }$

Hence,

ac = 25 meters ( hypotenuse )

So,

$\large{\boxed{\mathsf{Total \; displacement = 25\;meters }}}$

Conclusion :-

We can conclude that,

Total distance = 35 meters

Total displacement = 25 meters

So,

The shortest path is the diagonal path i.e. ac , instead travelling from a to b then b to c .