For such a potential, the transmission coefficient does not have the simple form |f| 2/|a| 2 because the potential does not go to zero as x → [infinity]. as a result, the transmitted wave travels at a different speed. show that in this case t = q e−v0 e |f| 2 |a| 2 . do this by noting that t is the probability of finding the wave in x > 0 relative to some incident probability in x < 0. for a plane wave, we can define an incident probability in a finite region – for example, in a particular area over a time interval dt. use this to argue that t = |f| 2 |a| 2 vt vi where vt , vi are the velocities of the transmitted and incident waves, and then use your knowledge of the velocity of a plane wave in terms of its energy.

In the middle of the night you are standing a horizontal distance of 14.0 m from the high fence that surrounds the estate of your rich uncle. the top of the fence is 5.00 m above the ground. you have taped an important message to a rock that you want to throw over the fence. the ground is level, and the width of the fence is small enough to be ignored. you throw the rock from a height of 1.60 m above the ground and at an angle of 54.0 degrees above the horizontal. part a part complete what minimum initial speed must the rock have as it leaves your hand to clear the top of the fence? express your answer with the appropriate units. part b for the initial velocity calculated in the previous part, what horizontal distance beyond the fence will the rock land on the ground?