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

Question #100473

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


1
Expert's answer
2019-12-16T11:05:30-0500

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 iˉ and jˉ\bar {i} \space and \space \bar {j}


iˉ=East\bar {i} = East


iˉ=West- \bar {i} = West

jˉ=north\bar {j} = north

,


jˉ=South- \bar {j} = South

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


Initial Velocity=50jˉInitial \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 Velocity=50iˉFinal \space Velocity = - 50 \bar{i}

Now,


Change in velocity (Δv) = Final velocity – Initial velocity = 50iˉ50jˉ- 50 \bar{i} - 50 \bar {j}


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


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


Answer: Yes


Change in velocity = 50iˉ50jˉ- 50 \bar{i} - 50 \bar {j}

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


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