Question

A 5.00 kg block is moving at 3.00 m/s along a frictionless table and collides with a 2.00 kg block that is initially at rest. The two blocks stick together and then slide up a 20.0 ◦ frictionless inclined plane. What is the maximum distance the two blocks slide up the incline?

Answer 1

The principle of conservation of momentum is used

initial momentum

where:

Initial velocities of each block

initially at rest

masses

Final momentum

where

  It is the final velocity of both blocks

as momentum is conserved

expression for vf

remember

evaluated numerically

  speed of both blocks

Now the vertical height is calculated:

mechanical energy at the bottom is just kinetic.

remember

the final speed is the initial shock of both going up the slope

mechanical energy at the top is only potential

where:
It is the acceleration of gravity
It is the vertical height

finally

as the mechanical energy is conserved

simplifying

evaluated numerically

to find the distance traveled on the inclined plane