What Is the Velocity After a Cork Ball and Dart Collide?

[loba333]

Homework Statement

A cork ball of mass 100 g at rest is released from a height of 8.5 m above the launch
point of a 300 g dart which is projected vertically upwards with an initial velocity of
12 m s–1. Upon impact, the cork ball and the dart stick together. Calculate their velocity
immediately after the collision.

Homework Equations

m₁v₁=m₂v₂
v=u+at
V²=u² +2as

The Attempt at a Solution

m trying to work out how to do this. I am thinking put two equations equal to each other in respect to time, as time will be the samwe both of them when they collide, I am just having trouble finding out which equations to use

Sorry in the title i say elastic when its inelastic

 

[madah12]

first figure out the velocity of the cork just before the impact ,and is it really elastic collision if they stick together?

 

[loba333]

how am to figure out the velocity when i don't know where where or when they collide ?

 

[loba333]

the velocity before it collides will be V =sqrt(2as)
but i don't know the height its collides at ie S it collides at

 

[madah12]

you have the height...

 

[loba333]

yeh but that's the height of the entire system not the height between the collision and the top.

Say we do work out this velocity, it will be the final velcity of the ball once traveled 8.5m. how can we use this to then help us work out where and or when they collide ?

Thanks

 

[madah12]

yeh but that's the height of the entire system not the height between the collision and the top.

Say we do work out this velocity, it will be the final velcity of the ball once traveled 8.5m. how can we use this to then help us work out where and or when they collide ?

Thanks

yes sorry,
They collide when they have the same position so for the ball y=y0-.5gt^2
and for the dart y=v0t-.5gt^2 solve for t then calculate the velocities of both particles then use the none elastic momentum equation.