Travelling in an elevator (not freefalling)

[danimation3d]

Hi all,
I'm trying to solve a very trivial question my friends have...
If one was travelling upward in a regular elevator, and the elevator was to suddenly stop, would there be enough momentum for the occupant to hit their head on the ceiling?
We're assuming there is only one occupant, who is 70kg, and the elevator is travelling at a rate of 2 meters per second.
If someone could show me how to work this one out, it would be much appreciated

Thanks

Dan

 

[serds]

First of all, the occupant has the kinetic energy of E_k=(1/2)*m*v² with m=Mass in kg v= speed in m/s
If the elevator stops E_k converts to potential Energy E_p= m*g*h with g = 9,81 m/s² and h = height.
Now set E_k= E_p​ and transform it to h = .... to figure out how high the occupant will get.

 

[Deleted member 4993]

Another way:

When elevator suddenly stops, you are moving upwards with a speed of 2 m/s.

If throw ball up with a speed of 2 m/s, how high the ball would go? standard Galileo's equation:

v² = u² + 2as → 0 = 2² - 2*9.81*s → s = 2/9.81 = ~ 0.2 m.

In standard elevator, for a standard person there should be enough headroom > 20 cm.