A projectile fired out at an angle ?, above the horizontal. The initial speed is

Question

A projectile fired out at an angle ?, above the horizontal.
The initial speed is Vo.

1. Find the range R.
2. If the projectile explodes at the point where x=3/4R into two pieces and if a piece with mass 1/4m lands at x=1/2R. Where does the other part land?

A projectile fired out at an angle ?, above the horizontal. The initial speed is Vo. Find the range R. If the projectile explodes at the point where x=3/4R into two pieces and if a piece with mass 1/4m lands at x=1/2R. Where does the other part land?

Explanation / Answer

1 . finally in vertical ,
using h = ut + at^2 /2

0 = v0sin?.t - g x t^2 /2

t = 2v0sin? / g

in horizontal ,

R = v0cos? x t = 2v0v0sin?cos? / g     = v0^2 . sin2? / g

2. at x = 3/4R

t = x/v0cos? = 3 (v0^2 . sin2? / g )/ 4v0cos? = 3v?sin?/2g

in horizontal ,

its center of mass will land on R .

so m/4 *( R/2)   = 3mx/4

x = 3R/2

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