Answer to Question #100473 in Mechanics | Relativity for s hota

Question

a motor car is going due north at a speed of 50km per hour. it makes a

900 left turn without changing the speed. the change in the velocity of the car is about

Answer 1

Mechanics | Relativity

We need to find the change in the velocity of the car .

Solution:

We can consider these velocities on an xy - plane with the vectors $\bar {i} \space and \space \bar {j}$

$$\bar {i} = East$$

$$- \bar {i} = West$$

$$\bar {j} = north$$

,

$$- \bar {j} = South$$

Initial Velocity = a motor car is going due north at a speed of 50km per hour.

$$Initial \space Velocity = 50 \bar {j}$$

Final velocity = it makes a 90 Degrees left turn without changing the speed

= It moves in the direction of west with the speed 50 km/h

$$Final \space Velocity = - 50 \bar{i}$$

Now,

Change in velocity (Δv) = Final velocity – Initial velocity = $- 50 \bar{i} - 50 \bar {j}$

$- \bar {i}$ direction (west) and $- \bar {j}$ direction (south), so the total change in velocity will be pointing towards the southwest.

$|\Delta V| = \sqrt {(-50)^2 + (-50)^2} = \sqrt {2500+2500} = \sqrt {5000} = 70.7 \space kmph$

Answer: Yes

Change in velocity = $- 50 \bar{i} - 50 \bar {j}$

$|\Delta V| = 70.7 \space kmph$