Which Coin Hits the Bottom of the Lift Shaft First?

[AllenHe]

Homework Statement

A lift is traveling upwards at constant speed. As it passes the second floor,a passenger frops coin A through an old-fashioned gate grille. At exactly the same time, a person standing on the second floor landing drops coin B through the gate grille at the landing. Which coin, A or B(if either),reaches the bottom of the lift shaft first?Which if (either) has the greater speed on impact?

Homework Equations

The Attempt at a Solution

 

[Dick]

I think everyone would like to hear your thoughts about the this. I.e. you should make some effort to solve it!

 

[AllenHe]

My teacher told me that when the passenger on the lift drops the coin, the coin is still experiencing an upward acceleration.So its velocity will be slower than the person who drops the coinB on the second floor landing.
But I checked the answer at the back of the book, it says that Coin B will have a greater speed on impact,but it also said that Coin A will reach the bottom first.That's a bit confusing.

 

[Hootenanny]

My teacher told me that when the passenger on the lift drops the coin, the coin is still experiencing an upward acceleration.So its velocity will be slower than the person who drops the coinB on the second floor landing.
But I checked the answer at the back of the book, it says that Coin B will have a greater speed on impact,but it also said that Coin A will reach the bottom first.That's a bit confusing.

Let's clear up a few things. The coin in the lift is not accelerating, since the lift is traveling at constant speed. At the point of release, coin A will have some non-zero upward velocity and so will continue to move vertically upwards for some time. Coin B in contrast, is initially stationary and therefore will fall straight down. Upon release, both coins will experience the same acceleration (-g) and therefore will accelerate at the same rate. Therefore, coin B will hit the ground first. Try it yourself, throw a ball upwards and at the same time drop another ball - which hits the ground first?

As for which coin has the greatest velocity, when coin A reaches the peak of its trajectory (i.e. when it stops before falling back to earth), it will be higher than where coin B began its fall to earth. Therefore, coin A will have more potential energy than coin B. When both coins hit the floor, their potential energies will be equal, with the change being converted to kinetic energy. Therefore, coin A will have greater speed on impact.

 

[AllenHe]

Im getting it.But in the book, it said that CoinA will reach the bottom first, and coin B has the greatest speed on impact.

 

[Hootenanny]

Im getting it.But in the book, it said that CoinA will reach the bottom first, and coin B has the greatest speed on impact.

Then the book is incorrect. It is precisely the opposite: Coin A has the greatest speed on impact and Coin B will reach the bottom first.