Aprojectile of mass moving with speed in the direction strikes a stationary target of mass head-on. the collision is elastic. use the momentum principle and the energy principle to determine the final velocities of the projectile and target, making no approximations concerning the masses. (use the following as necessary: , , and .)
[tex]v''=\frac{2m_{1}v_{1}}{m_{1}+m_{2}}[/tex]
[tex]v' = \frac{m_{1}-m_{2}}{m_{1}+m_{2}}v_{1}[/tex]
Explanation:
first mass, m1
second mass, m2
initial velocity of m1 is v1.
initial velocity of m2 is zero.
Let the final velocity of m1 is v' and the final velocity of m2 is v''.
Collision is elastic so the coefficient of restitution is 1.
By using the conservation of momentum
m1 x v1 + m2 x 0 = m1 x v + m2 x v''
m1 v1 = m1 v' + m2 v'' .... (1)
by the formula of coefficient of restitution
[tex]1=\frac{v''-v'}{v_{1}-0}[/tex]
v1 = v'' - v' .... (2)
So, v' = v'' - v1 put in equation (1)
m1 v1 = m1 x (v'' - v1) + m2 v''
m1 v1 = m1 v'' - m1 v1 + m2 v''
2 m1 v1 = (m1 + m2) v''
[tex]v''=\frac{2m_{1}v_{1}}{m_{1}+m_{2}}[/tex]
so,
[tex]v' = \frac{2m_{1}v_{1}}{m_{1}+m_{2}}-v_{1}[/tex]
[tex]v' = \frac{m_{1}-m_{2}}{m_{1}+m_{2}}v_{1}[/tex]
Compatible and speedy
net primary productivity
Explanation: i just took my test and this was correct!