Elastic collision in one dimension

[lone21]

Homework Statement

A Pendulum weighs .5kg and has a string length of 70cm swings from a horizontal position downwards to hit a block that weighs 2.5 kg and is on a frictionless plain. Calculate the speed of both the ball and the block after the elastic collision.

Homework Equations

mgh=.5mV^2
conservation of momentum
m1V= m1V1+m2V2
conservation of kinetic energy
.5m1V^2=.5m1V1^2+.5m2V2^2

The Attempt at a Solution

I used the first equation to solve for the initial velocity of the pendulum, which is 3.7m/s.
From here comes the elastic collision part.
I try to use both conseravation equations and substitute for one of the variables by solving for either V1 or V2 in either equation and thus substituting. However, when i try to solve it that way it ends up canceling out.
I know there is an equation for one dimension elastic collisions, but my professor says we can't use it unless we write the derivation of it, and that is a tedious thing to do and is rather lengthy.

Please help, ask questions if things are unclear

 

[rl.bhat]

Homework Statement

A Pendulum weighs .5kg and has a string length of 70cm swings from a horizontal position downwards to hit a block that weighs 2.5 kg and is on a frictionless plain. Calculate the speed of both the ball and the block after the elastic collision.

Homework Equations

mgh=.5mV^2
conservation of momentum
m1V= m1V1+m2V2...(1)
conservation of kinetic energy
.5m1V^2=.5m1V1^2+.5m2V2^2...(2)

You can rewrite eq.(1) as
m₁v - m₁v₁= m_2v2...(3)
Similarly you can rewrtie eq.(2) as
m₁v^2 - m₁v^2₁= m_2v^22..(4)
From 3 and 4 you can get
(v - v₁)/v^2 - v₁^2= v[/SUB]2[/SUB]/v[/SUB]2[/SUB]^2
After simplification you get
(v + v₁) = v₂
Substitute the value of v₂ in equation (1) and solve for v₁.