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

A: #usecthetasecalpha#
B: #usecthetasinalpha#
C: #ucosthetasecalpha#
D: #usinthetasecalpha#
PLEASE EXPLAIN EACH AND EVERY STEP

1 Answer
P dilip_k
Aug 7, 2017

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

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

The vertical component of the velocity after time #t# will be #vsinalpha#

But the horizontal component remains unaltered as #ucostheta#

So #vcosalpha=ucostheta#

#=>v=1/cosalphaxxucostheta=ucosthetasecalpha#

So option C is accepted

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