A projectile is fired with a speed u at an angle $θ$ $theta$ with the horizontal. Its speed when its direction of motion makes an angle $α$ $alpha$ with the horizontal is?

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A projectile is fired with a speed u at an angle $θ$ $theta$ with the horizontal. Its speed when its direction of motion makes an angle $α$ $alpha$ with the horizontal is?

A: $u sec θ sec α$ $usecthetasecalpha$
B: $u sec θ sin α$ $usecthetasinalpha$
C: $u cos θ sec α$ $ucosthetasecalpha$
D: $u sin θ sec α$ $usinthetasecalpha$
PLEASE EXPLAIN EACH AND EVERY STEP

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Answer 1 · 2017-08-07T15:50:43

Let the velocity of projection of the object be u with angle of projection $θ$ $theta$ with the horizontal direction.
The vertical component of the velocity of projection is $u sin θ$ $usintheta$ and the horizontal component is $u cos θ$ $ucostheta$

Now if t be the time after the projection of the projectile, its direction of velocity makes angle $α$ $alpha$ with the horizontal.Let the velocity of the projectile after t sec be $v$ $v$

The vertical component of the velocity after time $t$ $t$ will be $v sin α$ $vsinalpha$

But the horizontal component remains unaltered as $u cos θ$ $ucostheta$

So $v cos α = u cos θ$ $vcosalpha=ucostheta$

$\Rightarrow v = \frac{1}{cos α} \times u cos θ = u cos θ sec α$ $=>v=1/cosalphaxxucostheta=ucosthetasecalpha$

So option C is accepted

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A projectile is fired with a speed u at an angle $θ$ $theta$ with the horizontal. Its speed when its direction of motion makes an angle $α$ $alpha$ with the horizontal is?

A: $u sec θ sec α$ $usecthetasecalpha$
B: $u sec θ sin α$ $usecthetasinalpha$
C: $u cos θ sec α$ $ucosthetasecalpha$
D: $u sin θ sec α$ $usinthetasecalpha$
PLEASE EXPLAIN EACH AND EVERY STEP

1 Answer

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A projectile is fired with a speed u at an angle $θ$ $theta$ with the horizontal. Its speed when its direction of motion makes an angle $α$ $alpha$ with the horizontal is?

A: $u sec θ sec α$ $usecthetasecalpha$
B: $u sec θ sin α$ $usecthetasinalpha$
C: $u cos θ sec α$ $ucosthetasecalpha$
D: $u sin θ sec α$ $usinthetasecalpha$
PLEASE EXPLAIN EACH AND EVERY STEP