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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)
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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