A shell is shot with initial velocity [tex]\vec{}v_{0}[/tex] is 20ms[tex]^{-1}[/tex] at an angle [tex]\vartheta[/tex] = 60 degrees. At the top of the trajectory, the shell explodes into two fragments of equal mass. Fragment1 has a speed of 0 immediately after the explosion and falls vertically. How far from the gun does fragment2 land assuming terrain is level and there is no air drag?(adsbygoogle = window.adsbygoogle || []).push({});

Equations used:

F = ma

v[tex]^{2}[/tex] = v(of origin)[tex]^{2}[/tex] a + 2a(y-y[tex]_{o}[/tex])

p = mv

Initial middle

p=20ms[tex]-{1}[/tex]m p = [tex]\frac{1}{2}[/tex]mv + [tex]\frac{1}{2}[/tex]m x 0

=> 20m => [tex]\frac{1}{2}[/tex]mv + [tex]\frac{1}{2}[/tex]mx0

=> 20m = [tex]\frac{1}{2}[/tex]mv

=> 20 = [tex]\frac{0.5mv}{m}[/tex] = [tex]\frac{1}{2}[/tex]v = 40ms[tex]-{1}[/tex]

so the middle position is p = 40ms[tex]-{1}[/tex]

breaking this down to x y components:

for x:

cos[tex]\vartheta[/tex] = [tex]\frac{x}{20}[/tex]

cos [tex]\vartheta[/tex] x 20 = x

[tex]\frac{1}{2}[/tex] x 20 = x

x = 10

for y:

sin[tex]\vartheta[/tex] = [tex]\frac{y}{20}[/tex]

sin[tex]\vartheta[/tex] x 20 = y

[tex]\sqrt{\frac{3}{2}}[/tex] x 20 = y

[tex]\frac{20 x [tex]\sqrt{3}[/tex]}{2}[/tex] = 10 x [tex]\sqrt{3}[/tex]

y = 10 x [tex]\sqrt{3}[/tex]

using v[tex]^{2}[/tex] = v[tex]_{o}[/tex][tex]^{2}[/tex] a + 2a(y-y[tex]_{o}[/tex])

0 = (10 x [tex]\sqrt{3}[/tex])[tex]^{2}[/tex] + 2 x 9.8ms[tex]-{1}[/tex](y - 0)

0 = 100 x 3 + 2 x 9.8 x y

y = [tex]\frac{300}{19.6}[/tex] = 15.3

fragment1 dropped from a height of 15.3 meters

I am lost as to what equation to use to calculate the distance fragment 2 traveled from here. I know its simple but somehow I am not able to think of what to do next...... I need the distance in the x direction that fragement2 traveled.

hints??

thanx!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Shell fragments exploding - NSL for system of particles

**Physics Forums | Science Articles, Homework Help, Discussion**