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Prove That The velocity of the projectile at any t during its motion is given by v = Square Root (u^2+g^2*t^2-2ugt*Sin Theta)

Prove That


The velocity of the projectile at any t during its motion is given by


v = Square Root (u^2+g^2*t^2-2ugt*Sin Theta)


 

Grade:9

1 Answers

SOURAV MISHRA
37 Points
8 years ago

to prove this qusetion requires simple vector addition.

just imagine that at any instant the net velocity of the projectile is the superposition of two velocities:

1. the projection velocity u inclined at θ to the horizontal.

2. a vertically downward veloctiy equal to gt which a freely falling body would acquire when it has fallen for time t.

the angle between these vectors equals 90° + θ.

so the net velocity at any time comes out to be v = {u2 + g2t2 - 2ugtsinθ}(1/2).

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