A feather dropped on the moon On the moon, a feather will fall...

Question

A feather dropped on the moon On the moon, a feather will fall to the ground at the same rate as a heavy stone. Suppose a feather is dropped from a height of 40 m above the surface of the moon. Its height (in meters) above the ground after t seconds is s = 40−0.8t². Determine the velocity and acceleration of the feather the moment it strikes the surface of the moon.

Accepted Answer

Hello there. Today we're gonna solve the following practice problem together. So first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. A stone is dropped from a cliff into the sea, and its height in meters above the water after T seconds is given by S equals 80 minus 5T 2. Find the velocity and the acceleration of the stone just before it hits the water. Awesome. So it appears for this particular problem, we're asked to solve for two separate answers. Our first answer is we're trying to figure out the velocity of the stone just before it hits the water, and our second answer is we're trying to figure out the acceleration of the stone just before it hits the water. So now that we know that we're solving for two separate answers for the velocity and the acceleration of this particular stone, let's read off our multiple choice answers to see what our final answer pair might be, noting that our units for the velocity are in meters per second, and the units of measurement for acceleration are meters per second squared. So A is -40 and -5. B is -50 and 10, C is -40 and 10, and finally D is -40 and 10. OK. So first off, we need to focus our attention on the time when the stone hits the water. So we need to note that the stone hits the water when S equals 0. So we need to note once again, S equals 0 means that's when the stone hits the water. So meaning we could go ahead and write that. 80 minus 5T 2 is equal to 0, so -5 T2 is equal to -80, which will mean when we rearrange this equation to isolate and sour T all by itself, we will find that T. is equal to 4 seconds. I've gone ahead and skipped a few steps because you you should understand basic algebra to help rearrange this to isolate and solve for T on one side of the equation. So when you do that, you will find that -5 T2 equals -80 will be when you isolate and solve for T, you'll find that T is equal to 4 seconds. And now our next step is we need to find the velocity of the stone. So we need to recall and note that the velocity in this for the velocity, we could find that by taking the first derivative of the height functions with respect to time T. So once again, you can figure out the velocity equal like the velocity by taking the first derivative of the height function. S with respect to T, once again, so taking the first derivative of S with respect to T will give us that V the velocity is equal to DS by DT, which is equal to D by DT of 80 minus 5T 2, which is equal to when you take the first derivative negative 10 T. So now to find the velocity of the stone when it hits the water, so this is when T is equal to 4 seconds. We will get that V is equal to -10T, which is equal to -10 multiplied by 4, because you're plugging in a value of 4 in for T, and when we do that, you will find that it's equal to -40 m per second, and that is our first answer for the velocity V. Hooray, we did it. So now, we need to figure out the second derivative of S with respect to T, and that will help us find our acceleration, because our acceleration function, so in order to find acceleration, all you need to do is take the second derivative of S with respect to T, meaning you just need to take the derivative of the velocity. So that means You need to take our acceleration, which is gonna be denoted by A, so A, the acceleration is equal to D by DT. Of VFT, which is our velocity function. Which is equal to D by DT of -10T, which is equal to -10 m per second squared, which is our second and final answer for the acceleration. A. Hooray, we did it. So therefore, the acceleration of the stone just before it hits the water is -10 m per second squared. So that means without a doubt, our final answer pair has to be multiple choice answer letter C, which once again states that the velocity is -40 m per second and the acceleration is -10 m per second squared. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

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