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Law of Conservation of Mechanical Energy

30 A particle...

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30 A particle is projected with a velocityv = (3i-1+2k) m/s and a constant accelerationacting on the particle is ä (-6i+2j-4k) m/s.Then the path of projectile is(1) Straight line(2) Circle(3) Parabola(4) Ellipse

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Q. A particle is projected with a velocity of

\sqrt{7} {ms}^{- 1}

60^{\circ}

with horizontal. Find the average velocity of the projectile between the instants of point of projection and reaching the highest point.

Q. Find the shortest distance between the skew lines

r = (6 i + 2 j + 2 k) + t (i - 2 j + 2 k)

F = (- 4 i - k) + s (3 i - 2 j - 2 k)

where s,t are scalars.

Q. Forces acting on a particle have magnitudes of

5, 3

1

units and act in the direction of the vectors

6 i + 2 j + 3 k, 3 i - 2 j + 6 k

2 i - 3 j - 6 k,

respectively. They remain constant while the particle is displaced from the point

A (2, - 1, - 3)

B (5, - 1, 1)

. The work done is equal to

Q. The shortest distance between the skew lines

\to r =_{1} + t_{1} and \to r =_{2} + n - \to a_{2}, where_{1} = 9 j + 2 k,_{1} = 3 i - j + k,_{2} = - 6 i - 5 j + 10 k,_{2} = - 3 i + 2 j + 4 k

3 \sqrt{a}

. Then the value of

a

Q. Forces acting on a particle have magnitudes

5, 3, 1 k g . w t

and act in the directions of the vectors

6 i + 2 j + 3 k, 3 i - 2 j + 6 k

2 i - 3 j - 6 k

respectively.These remain constant while the particle is displaced from A (4, -2, -6) to B (7,-2,-2). Find the work done.

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