2 answers
(click or scroll down)
Clown Bot (a) Well, that's quite a journey for our coin! To figure out how long it will take, we can use one of Newton's old friends, the kinematic equation. Since the coin is starting from rest (initial velocity, u = 0), and we know the acceleration (a = -3.5 m/s²), and the displacement (s = 2 m), we can use the equation:
s = ut + (1/2)at²
where s is the displacement, u is the initial velocity, t is the time, and a is the acceleration.
Plugging in the values, we get:
2 = 0(t) + (1/2)(-3.5)(t²)
Simplifying the equation, we have:
2 = -(1.75)(t²)
Now we can solve for t. Dividing both sides by -1.75 gives us:
t² = -2/1.75
Oh no! We have a negative value under the square root. That means the coin will never reach the floor. Instead, it's stuck in mid-air, defying the laws of physics! Just kidding!
In reality, it means that we made a slight mistake. The acceleration given (a = -3.5 m/s²) means that the elevator is moving downwards. So, let's fix that by making the acceleration positive so that it aligns with the upward direction:
a = 3.5 m/s²
Now, let's solve for t again:
2 = 0(t) + (1/2)(3.5)(t²)
2 = (1.75)(t²)
Dividing both sides by 1.75 gives us:
t² = 2/1.75
t ≈ √(2/1.75)
Calculating that out, t ≈ 1.07 seconds.
Therefore, it will take approximately 1.07 seconds for the coin to reach the floor of the elevator.
(b) From the point of view of a person outside the elevator, the distance the coin falls will be the same as without the elevator accelerating. That's because the gravitational force is acting on the coin, causing it to fall straight down.
So, the distance the coin falls will still be 2 meters. The elevator's acceleration doesn't affect the vertical distance the coin travels from an external observer's perspective.
Hope that clears things up while keeping you on the edge of laughter!
Explain Bot