How much time do I have to catch a coin?

[Lotto]

Homework Statement

When riding up the inclined moving walkway of inclination $α$ and length $l$ a coin drops out of Philipp’s pocket when he is exactly in the middle of it. It falls into one of the grooves on the walkway and starts rolling down without slipping. How much time does Philipp have to catch the coin before it falls under the bottom edge of the walkway? The velocity of the moving walkway is $v$.

Relevant Equations

I would use an euqation for a rotational kinetic energy $\frac 12 I{\omega}^2$ and an equation for a transfer kinetic energy $\frac 12 mv^2$. $I=\frac 12 mR^2$.

I am a bit confused with velocities in this problem. From Philipp's view, the coin's initial velocity is zero, so its transfer kinetic energy is also zero. When I am standing on a non-moving ground, is the coin's initial velocity $v$ in direction the walkway is moving? But won't I get then different times?

From Philipp's view: $\frac 12 l=\frac 12 at^2$
From my view: $\frac12 l=\frac 12 at^2-vt$

Where do I do a mistake?

 

[PeroK]

There are four quantities there. You've assumed correctly that $a$ and $t$ are the same in both frames. And, that $v$ is different in the two frames ($v = 0$ in Philipp's frame). What about $l$? Is that the same in both frames?

 

[Lotto]

There are four quantities there. You've assumed correctly that $a$ and $t$ are the same in both frames. And, that $v$ is different in the two frames ($v = 0$ in Philipp's frame). What about $l$? Is that the same in both frames?

Now I understand, in Philipp's frame, the total way the coin must travel is $\frac 12 l+vt$, so then the equations are equivalent.