Free Fall vs constant speed

[godkills]

While riding on an elevator descending with a constant speed of 3.0 m/s, you accidentally drop a book from under your arm.
How long does it take for the book to reach the elevator floor, 1.2 m below your arm?
What is the book’s speed when it hits the elevator floor?My question is why is 3.0 m/s in constant speed ignored in this question?

We are using the equation x = x₀ + v₀ + 1/2(a)(t²)

Why is that v₀ is not plugged in? When 3.0 m/s is v₀ (velocity).

Since velocity here is descending then the velocity in this question is -3.0 m/s correct?

also i am having problem solving part b in which i don't know where to begin

 

[tvavanasd]

Both the elevator floor and the book are within the same inertial frame of reference (both are moving at a constant speed in a straight line). You are interested in the relationship between them, not that with objects outside that frame.
Vo of the book relative to the floor is zero.
The sign that you give the velocity must agree with that for position and acceleration (if you call down positive, acceleration down is also positive).
Once you know the time for the book to fall 1.2 m, can you not calculate speed (or velocity) based on other constant acceleration equations?

 

[godkills]

Vo of the book relative to the floor is zero.

Is that because the book is in free fall meaning that only gravity is affecting it and that the book has no speed only acceleration which is gravity?

Free fall (free from any effects other then gravity so speed is one of the effects correct?)

For part (b) I keep getting 7.9 but the answer is 4.8

 

[tvavanasd]

Remember to show units in your answers.

If you were inside the elevator, you would not be able to tell whether it was at rest, or moving up or down at a constant speed (assuming it's motion is smooth).

All motion of interest in this question is with respect to the inside of the elevator (the inertial frame), not the building.

In this case, you should completely ignore the velocity of the elevator. True, the velocity of the book when it hits the floor relative to the building is about 7.85 m/s, but the book will actually hit the floor of the elevator at approximately 4.85 m/s (relative to the floor). This is representative of how hard it will hit the elevator floor (7.85 m/s is not).

I get:
t = sqrt (2 * 1.2 / 9.8)
t = 0.495 s

v = a * t
v = 9.8 * 0.495
v = 4.85 m/s

 

[rwisz]

In this scenario, the elevator is moving at a constant speed of 3.0 m/s, which means that the acceleration is 0 m/s^2. In free fall, an object is accelerating due to the force of gravity, but in this case, the book is not falling freely because it is moving with the elevator.

To calculate the time it takes for the book to reach the elevator floor, we can use the equation x = x0 + v0t + 1/2at^2, where x0 is the initial position, v0 is the initial velocity, a is the acceleration, and t is the time. In this case, x0 = 0 m, v0 = 0 m/s, a = 0 m/s^2, and x = 1.2 m. Plugging these values into the equation, we get:

1.2 m = 0 m + 0 m/s * t + 1/2 * 0 m/s^2 * t^2

Simplifying, we get:

1.2 m = 0 m + 0 m/s * t + 0 m/s^2 * t^2

1.2 m = 0 m + 0 m/s * t + 0 m/s^2 * t^2

1.2 m = 0 m + 0 m/s * t + 0 m/s^2 * t^2

We can see that the only variable left is t, so we can solve for t by rearranging the equation:

t = √(2 * x / a)

Plugging in the values, we get:

t = √(2 * 1.2 m / 0 m/s^2) = √(2 * 1.2 m) = √2.4 m = 1.549 m/s

Therefore, it will take approximately 1.549 seconds for the book to reach the elevator floor.

Now, to calculate the speed of the book when it hits the elevator floor, we can use the equation v = v0 + at, where v is the final velocity, v0 is the initial velocity, a is the acceleration, and t is the time. In this case, v0 = 0 m/s, a = 0 m/s^2, and t = 1.549 s. Plugging these values into the equation,