Question

A motor car is going due north at a speed of 50$km/h$.It makes a 90 left turn without changing the speed. The change in the velocity of the vehicle is
A. 50 $km/h$ towards west
B. 70 $km/h$ towards south-west
C. 70 $km/h$ towards north-west
D. Zero

Answer 1

Hint:In such questions we need basic concepts of velocity and vector addition and applying it to find the required change in velocity.

Complete step by step answer:

Given, ${v_f}$ , ${v_f}$
Initial velocity = ${v_f}$​=50j
Final velocity =​${v_f}$=−50i
 Therefore, Change in velocity = Δv=${v_f}$−${v_i}$​=−50i−50j
Negative x- means west direction and negative y-component means south direction. Hence resultant velocity is in the south-west direction.
Magnitude of change in velocity = \[(( - {50^2}) + ( - {50^2}))\;\]= 70. 71 km/h
Hence, the answer is 70 km/h and the direction is south-west direction.
The correct option is B.

Note – For such types of questions we need to take care in vector subtraction and direction of the given vector and the resultant vector. For such a question we should draw a rough sketch of the question in order to better understand the question.