Question

In going from one city to another, a car travels 75 km north, 60 km north-west, and 20 km east. The magnitude of displacement of the car in travelling between the two cities will be:- (take √2 = 1.4)
a) 170 km
b) 137 km
c) 119 km
d) 140 km
Show the working as well.

Answer 1

Answer is 119km, PFA for the solution

Answer 2

Answer:

The displacement of car between two cities will be 119 km

C is correct.

Explanation:

For naming of points and distance. Please refer attachment.

In going from one city to another, a car travels 75 km north

Start from origin, O: (0,0) to reach a point A(75,0)

then move 60 km north-west and reach at point B

At last 20 km east and reach at point C

Displacement of car from starting point = OC

Using distance formula to find the distance of OC.

First, we have to find the coordinate of O and C

Coordinate of O(0,0)

x-coordinate of C:  BD-BC

y-coordinate of C: OA+AD

In ΔABD, ∠D=90°

$BD=AB\cos45^\circ$

$AD=AB\sin45^\circ$

where, AB is 60

Thus, $BD=60\cos45^\circ=30\sqrt{2}\approx 42$

$AD=60\cos45^\circ=30\sqrt{2}\approx 42$

x-coordinate of C:  42-20=22

y-coordinate of C:  75+42=117

Therefore, Coordinate C(22,117)

Now, we find the distance between O and C using distance formula.

$OC=\sqrt{(22-0)^2+(117-0)^2}$

$OC=\sqrt{14173}\approx 119$

Hence, The displacement of car between two cities will be 119 km