Question

A boy walks uniformly along the sides of a rectangular park of size 400m×300m , starting from one corner to other corner diagonally opposite . Which of the following statement is incorrect?
A) he has traveled a distance of 700m
B) his displacement is 700 m
C) his displacement is 500m
D) his velocity is not uniform throughout the walk.

Please help me with this and with steps...

Answer 1

As per given condition,

A boy walks uniformly along the sides of a rectangular park of size 400m×300m, starting from one corner to other corner diagonally opposite.

Assume a rectangular park ABCD having sides 400 m and 300 m respectively. (Take side AB and CD as 400 m and AD and BC as 300 m.)

Now,

Distance is defined as the total path covered by the body. Whereas, Displacement is defined as the shortest path travelled between the initial and final points.

In ∆ABC

By Pythagorean theorem,

H² = P² + B²

(AC)² = (BC)² + (AB)²

(AC)² = (400)² + (300)²

(AC)² = 160000 + 90000

(AC)² = 250000

AC = √250000

AC = 500

Therefore, the displacement of the boy is 500 m.

Also, Total distance covered by the boy = Sum of it's opposite sides i.e. length & breadth

= (400 + 300)m

= 700 m

Therefore, option b) his displacement is 700 m is incorrect.

Answer 2

★ Diagram

$\setlength{\unitlength}{1.5mm}\begin{picture}(5,5)\multiput(0,0)(0,22){2}{\line(1,0){22}}\multiput(0,0)(22,0){2}{\multiput(0,0)(0,4){6}{\line(0,1){2}}}\put(-3,-3){B}\put(-3,24){A}\put(23,-3){C}\put(-9,11){300\ m}\put(7.5,-3){400\ m}\end{picture}$

★ Solution

Let

• First point be A
• Final point be C
• Mid point be B

Given,

• Distance from A - B = 300m
• Distance from B - C = 400m

Distance from A - C = Total distance = A - B + B - C

→ Total distance = 300m + 400m

→ Total distance = 700m. ( option A )

Now, displacement : AC

Using Pythagoras theorem

→ 300² + 400² = AC²

→ 90000 + 160000 = AC²

→ √250000 = AC

→ AC = 500. ( option C)

Options A , C are right . Now , in the question we need to find incorrect options

Hence statement B is incorrect .

Here , we can't consider statement D is incorrect because we they didn't give time taken and we can't find it