All the smart guys in my physics class make me feel inferior. They said girls couldn't solve problems......

Question

I am not sure how to solve physics problems on my own, and this one especially baffles me. It is the following

1. A radioactive form of uranium has a half-life of 2.5x10^5 years.

what's the remaining mass of a 1.0g sample after t years


2. a tennis ball is dropped from a height of 10m. each time the ball touches the ground, it bounces up to about 45% of the max. heighut of the pervious bounce. determine its height after 5 bounces.


I want to impress the males in my class who think that girls can't be as smart so maybe they will accept me.

Answer 1

If that's your goal, then you seriously need to do the problems on your own. Even if it means reading the textbook. These are very simple and straightforward applications of basic formulas, it shouldn't be that hard for you if you try.

I'll help ya out with the second one.
Starting height: 10 m
After one bounce: 0.45 * 10m
After two bounces: 0.45 * 0.45 * 10m
After three bounces: 0.45 * 0.45 * 0.45 * 10m
After five bounces: (0.45)^5 * 10m

That's approximately 0.18 meters, or 18 cm.

Now you go do the first one. Here's a hint:
http://www.mathwords.com/e/exponential_decay.htm

Answer 2

I'm going to disregard your plea on the basis of proving the equality of your gender since that entire reason is bullshit (I know a girl who is far more intelligent than any of her male peers) and instead help you simply because you're a person who does not understand a bit of material regarding physics.

First, think about what a half-life is. Every t years, the amount of radioactive material is reduced by half. So, after one duration of half-life, you will have half as much material...or p/2 if you define p to be the original mass.
After two half-lives, you will have one quarter of material... or p/4
After three, you will halve it again and wind up with one-eighth... p/8
Notice something? The denominator is going up by multiples of two.

So, now you know that the number of remaining mass, n, will equal n = p / 2^h where h is a mysterious exponent that represents the effects of half-lives.

Take a closer look at h. We tend to look at half-lives in terms of years. Every radioactive material has a different length of a half-life, and fortunately this has been given to you already in the problem. Let's make up two variables... k and t. k will represent a constant that is based on the half life and t will represent the amount of time that has actually passed. We can say that k*t=h since this is how we are going to define these variables. Now, we know that the half-life is 2.5x10^5 years. This means that after that time, you will have p/2 (or p / 2^1) material, and therefore h will equal 1. Since h=1 and k*t = h, we can say that k*t = 1. Also, because of how we have set up the problem, t = 2.5x10^5 since this is how much time has passed.
This means k*2.5x10^5 = 1. Solve for k to get k = 2.5x10^(-5)

Now, we have n = p / 2^(k*t), so we can plug in for k to get
n = p / 2^(t*2.5x10^-5).
Also, we are given the value of p as 1.0g so we can plug that in to get

n = (1/2)^(t*2.5x10^-5)
And there is the function that you are looking for.

2)

This may seem totally unrelated to the previous, but this is actually a very similar problem. Each time it hits the ground, it bounces back up 45% or x.45 the previous height. That means that after the first bounce, it will return x.45 of the original, and after the second it will be x.45^2 the original and so on. If you represent the number of bounces with n, you can say that h = h[0] * (.45)^n where h is the most recent max height and h[0] is the original max height (which is 10m).

Plug in what you know to get h = 10*(.45)^5
Type that into a calculator to get the value of h and there will be your answer.



Don't seek acceptance. Do your best, that's all that anyone can ask of you, and push yourself -- you owe it to yourself to do so. Most importantly, use your mind; it's incredibly powerful and there isn't another one out there like it. You can overcome any obstacle in your path, whether it is physical, mental, or emotional... you just need to press on, believe in yourself, and use your brain. It's a wonderful thing; don't waste it.

Answer 3

2. 10*.45*.45*.45*.45*.45=.1845

The other one is physics, and you are in the math section.

BTW it's proven that men are better in science and math

Why did I get thumbs down? My math is right and my words are true. Honestly! Women are better at English in social studies and men are better at math and science. No lie!