Math, asked by vaishnavinadar2404, 1 year ago

A car travels 6 km towards north at an angle of 45 to the east

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Answered by HARISHKABILAN
1

A car travels 6 km towards north at an angle of 45 degree to the east and then travels distance of 4 km towards north at an angle of 135 degree to the east.How far is the point from the starting point .What angle does the straight line joining its initial and final position makes with the east?

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student-name Apurba Paul answered this

356 helpful votes in Physics, Class XII-Science

We can use vector sum to find out the final position of the car. To do this let us first find out the x and y component of the displacements

For first displacement we have

x componentd1x=6cos45°=62√y component is d1y=6sin45°=62√

Now for second displacement we have

x componentd2x=4 cos135°=−42√y component d2y=4 sin135°=42√

So total x component is dx=62√−42√=22√

and total y component is dy=62√+42√=102√

So the magnitude of the total displacement is dx2+dy2−−−−−−−−√=(22√)2+(102√)2−−−−−−−−−−−−−√=42+1002−−−−−−√=52−−√=213−−√km

and the angle is θ=tan−1(dydx)=tan−1⎛⎝102√22√⎞⎠=tan−1(5)=78.5°
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