The range of a projectile is affected by what?

1 Answer
Feb 25, 2018

Suppose, a projectile was projected with an initial velocity of #u# at angle #theta# w.r.t the horizontal.

So,it will go up due to its vertical component of velocity i.e #u sin theta# and then come down due to the effect of gravity.

At the same time it will proceed forwards due to its horizontal component of velocity i.e #u cos theta#

So,if it takes time #t# to reach the highest point,we can say, #0=u sin theta- g t# (using, #v=u-at#,at the highest point, #v=0#)

So, #t=(u sin theta)/g#

Now,the projectile will take the same time to come down to the ground,so total time of flight will be #(2u sin theta)/g#

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Now,if the projectile goes a distance #R# (range) horizontally,in that time,we can say, #R= u cos theta *(2u sin theta)/g= (u^2 sin 2 theta)/g#

So, we can see the range depends on the initial velocity of projection(#u#),angle of projection (#theta#) and acceleration due to gravitational force(#g#) (well the last one can be taken as constant for earth)