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Question

a projectile w/ mass .850 kg is shot up w/ speed of 20 m/s how high would it go if there was no air friction?

I was looking through my book for a possible explanation on this but none of the formulas could i find to do with height? it is hidden w/in a formula and didn't notice... please explain to me how to wrok this out... again id ont expect anyone to do it for me and just give me answer i really do want to learn this stuff but for some reason physics is hard for me... please help me set this up and understand why and how.....

also there is a second part to this problem where they give you a mx height and it says to determine magnitude of average force due to air resistance.... ill workt his out on my own but is there a formula you use for avg force due to air resistance... my book is absolutely no help when it comes to these homework problems thank you

Answer 1

OK. The first thing you do with any physics problem is consider what's going on. Don't worry about looking for formulas until you understand the problem.

You have a projectile. It has a mass of .85 kg.
It's not sitting still; it's shooting straight up into the air starting with a velocity of 20 m/s.

So would it keep going up and up and up indefinitely?
I hope you answered, "No, gravity would be pulling on it and would slow it down. It would only go up so high, stop, and fall back down toward the earth."

So we have a projectile with an initial velocity of 20 m/s moving straight up away from the earth. Gravity is pulling on it, and I'm thinking that its pulling directly down toward the earth, exactly opposed to the velocity vector. And I'm thinking that gravity exerts a relatively constant force on the projectile, doesn't it?

Do you remember seeing something about gravity exerting a force that is relatively constant as long as you don't get far from the surface of the earth? Many texts express it as F = m*g, where m is the mass of the object and g is the acceleration rate of gravity, which is roughly 9.8 m/s^2.

So you have a constant force problem. If you have a constant force you have a constant acceleration. In the case of gravity, it's a constant acceleration in the downward direction. The projectile is moving upward, so if it being pulled downward, the force of gravity is slowing it down (negative acceleration, or deceleration) and then accelerating it back toward the earth.

For constant acceleration problems, the velocity goes like:

V = vi + a*t, where vi is the initial velocity, a is the accleration and t is time.

Distance goes like:

D = vi*t + (1/2)*a*t^2, with the same definitions for vi, a, and t.

In this problem, if you want to know how far the project goes, you want to know how far will it travel until its velocity is zero. So you can calculate how much time that would take, using the velocity equation and then plug that time into the distance equation to calculate the distance traveled.

The only thing that's slightly tricky is that you have to be sure that you remember that the acceleration, a, is a negative value, because its slowing the projectile down.

so, vi = 20 m/s, a = g = -9.8 m/s^2, and V = 0. Plug those in and solve for t.

If I round 9.8 up to 10 m/s^2, I get t = 2 s

To calculate the distance plug the values into the distance equation, making sure that you are using negative accleration, and you should get 20 m.

For the part where they give you a max height, you have to make some assumption about the frictional force, ie, how it varies with speed. Since they are talking about average frictional force, that means that they are saying that you should neglect any speed dependence and just assume that there is a constant average frictional force for the entire distance traveled. So, now the total force acting on the projectile is not just Fg but is Fg + Ff, where Fg is the gravitational force and Ff is the frictional force. You will want to find the equivalent acceleration that will give that max height and then subtract g from it to find the acceleration due to friction. Ff = m*af (where af is the accleration of friction).

Answer 2

It is a problem in the conversion of energy in different forms. When shot up, the projectile has a kinetic energy of 1/2 MV^2. You know M and V, so you know the initial kinetic energy. At the top, it is not moving so all of its kinetic energy has been converted to potential energy having to do with its Mass, its height, and the attraction of gravity. But its the same amount of energy, so you can solve for H.

Answer 3

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