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## Projectile Motion

“A body is projected with velocity u with an angle with the horizontal. What is its average velocity when it crosses half of its max height”

1. the drawing on the left shows two vectors A and B, and the drawing on the right shows their components.

The scalar components of these vectors are:

When the vectors A and B are added, the resultant vector is R, so that RAB. What are the x– and y-components of R?
2. the displacement vectors A and B, when added together, give the resultant vector R, so that RAB. Use the data in the drawing to find the magnitude R of the resultant vector and the angle q that it makes with the +x axis.

In the first question as you can see that the X components (Ax and Bx being equal and opposite will cancel each other and therefore the X com ponent of the resultant is zero.

The Y components will add up and therefore the Y component of resultant = 3.4+3.4 = 6.8 m and this itself is the magnitude of the resultant as the X components have canceled out.

Hnit for Answer to the second question

## Resolution of Vectors

From: Vakas

Subject: Resolution with geometry
Message Body:
Dear sir,
I m not able to understand that when we resolute mg in a inclined plane that plane having angle theta,how does the vertical component goes through inclined surface & cos comp opp to N.
explain with geometry so that i don’t get confused in future in determining the two comps is right direction.

Ans:

In a right angled triangle,

$cos\theta =\frac{adjacent side}{hypotenuse}$

and

$sin\theta =\frac{opposite side}{hypotenuse}$

When mg is resolved into mutually perpendicular directions, one parallel to plane and the other perpendicular to the plane (opposite to the Normal reaction), the component which is adjacent to θ is the cos component and the one away from θ is the sine component.

Students find difficulty ,mainly in identifying the angle .

See the diagram below and try to analyze

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