Question

prove why a projectile goes furthest if it were projected on 45 degree.

Answer 1

This is also assuming no air resistance. That should be stated in the question.

Answer 2

This is only the case by assuming that air resistance is negligible, gravitational field lines are all parallel, that gravitational acceleration is constant everywhere and that you are shoot from a point on smooth, horizontal ground.
Given these conditions, let initial velocity of your projectile = v, angle of elevation = A, gravitational acceleration = g.
If the time spent airborne is t then\[t = \frac{2 v \sin A}{g}\]
and the if thehorizontal distance travelled is d then
\[d = \frac{2v ^{2}\sin A \cos A}{g}= \frac{v ^{2}\sin 2A}{g}\]
The maximum value of the sin function is 1 which is reached when the angle is 90 degrees. Therefore for d to be maximised, 2A=90 degrees and so A=45 degrees.

Answer 3

the range of the projectile is given by\[R=(u ^{2}\sin2\theta)/g\]
the maximum value of \[\sin \theta=1 for \theta=90\]
therefore fot max range \[2 \theta= 90\]
that is \[\theta=45\]

Answer 4

new here, so i dont know what is frac and /

Answer 5

do you have any reference website to explain. just curious.

Answer 6

i have no physics. but where can i find the website to simply understand it. he will be selected as best answerer

Answer 7

better if you check ABC physics part 1 physics class xi page 173 horizontal range last para

Answer 8

This website seems suitable: http://www.mathsrevision.net/alevel/pages.php?page=88.

Answer 9

If you're seeing frac and \ then your browser must be incorrectly displaying my formulae. This website's formula renderer interprets frac as a declaration of a fraction and uses \ to separate functions.

Answer 10

@ J_Ferdous

Look up Range or Horizontal Range or Projectile Rage in one of your physics books.

Answer 11

the basic understanding is distance = speed times time

\[distance = (u \cos A) \times \frac{2u \sin A}{g}\]

Answer 12

so your splitting the velocity into its up motion and down motion. its height determines how long it stays in the air (time)