5

Eacapa ValochyAK Wobject projected from the surlace the earth with speed3.67*104 ns. What its speed whenvery far from the earth? (Neglect air resistance:)Submiansyc...

Question

Eacapa ValochyAK Wobject projected from the surlace the earth with speed3.67*104 ns. What its speed whenvery far from the earth? (Neglect air resistance:)SubmiansycrTries 0/10

Eacapa Valochy AK W object projected from the surlace the earth with speed 3.67*104 ns. What its speed when very far from the earth? (Neglect air resistance:) Submiansycr Tries 0/10



Answers

A $1.0 \mathrm{kg}$ object is released from rest $500 \mathrm{km}$ ( $\sim 300$ miles) above the earth. a. What is its impact speed as it hits the ground? Ignore air resistance. b. What would the impact speed be if the earth were flat? c. By what percentage is the flat-earth calculation in error?

This guy. Should we have an object being ejected off the surface? Off the off At a nontrivial speed, he's feel sees 10 poll four meters per second. It's quite large. So the height that you will rise by will be a significant distance away, compared it to the radios off off. So we cannot just use simply MGH to find you. Quit this to the initial kinetic energy. I cannot do that because ah, the potential energy in this case, the genie gravitation acceleration would not be constant. So what we have to do is to use the general from off gravitational potential energy that is your goes to the thief. Gmm over. Ask where you are. Sorry. Just are to find what is in the show and final potential to get the kinetic energy. So any top we re just the maximum Haidt Kinetic energy is cereal. So the final, um city final energy total energy would just be the potential energy. The initial initial energy, however, includes both the initial potential energy as dost in the show Kinetic energy. This is because to native she I am over radio Softy off. All right. It is the object is just on the radius off your Saudi distance between the center of mass of the earth and the object must be your eight years off the off lusty kinetic energy, which is half times a mofo object. Tom Stephen L C squared. Just give it away. Here. The final potential energy IHS close to negative over. Videos off the earth Blast e height. English. Yes, Often. And so it is from this secretion we want too soft for hitch. So, you know, do that We need to first simply fire our equation bits by substituting devalues in so mess off both. Skipper, wish you this isn't any for velocity. Tend apart for mess off object we're going to can So the mess off the objects from the entire expression because the piers in off the terms so we can actually remove this? Uh I m Dismore him so no, we can substituting values, right? Used to have Toso GST gravitational constant. Yes, off the earth is given 6.37 six. So we're gonna do is we're going to multiply. Uh, this medias off earth plus heights to the left in sight. There were gonna be felt with this to expression right GM over r E and 1/2 the square black coffee square and the fight this over here it's so this expression should actually give us what point this is supposed to be negative. 0.6 im said about seven. So are plus each too close to G times. Mess off your roof well for 1.26% Powers seven Chase if you 0.99 x 10 12. 14 over 1.267 So even everything this, then we subject away and height hitch so subject of 80 radius off the off Just six months. 3 70% 46 There no hitch B 2.52 percent power seven meters

Here we have initial kinetic energy, plus any field potential energy. Plus the energy provided in the form of mechanical energy will be final, kinetic and potential energy that some of that here the initial kinetic energies half massive. The planet initiative US B squared minus potential is G and then it and art bulls later r e the US No mechanical energy is provided equals. Finally, the kinetic energy zero and the potential energy is G implant. It am art over r e does h. So now from over here we can put all the numbers and salt for age. And if you do that, age will come out to be 2.52 times 10 to the seven.

In this problem We have to calculate the maximum height reached by an object that has launched with the initial velocity 10 km/s. Now I like to start by converting the kilometers per second into the S. I units meters per second. So we can do that just by multiplying it by 10 to the three. Now we have our velocity in meters per second. Let me go ahead and multiply these and we have our velocity as 10 to the 4th m/s. Now I'll be using an energy approach to solve this problem because I feel it's the easiest and does not require the evaluation of any integral. So let's consider the total energy, let's call it T. Which is equal to the kinetic energy plus the potential energy. Now the kinetic energy is get just given by the Formula 1/2 Emily. Sward. While the potential energy for two gravitating bodies is given by the Formula G. M1 times M2 divided by R. Where R. Is the total distance between the two center of mass is Mhm. Not that there's a negative sign for the potential energy because gravity is an attractive force and gravitational potentials are always negative. So we can just start to substitute the values now. Yeah. So the mass of the object, we don't know The velocity is 10 to the 4th m/s. Mhm. Yeah. Yeah. For our first mass will keep the mass of the object which we don't know. So let's keep that as M. And M. two is the mass of the earth, the second gravitating body. And that's equal to 5.972. Yeah. And do 10 to the 24 kg. And we're going to divide this by the total separation of the center of mass. Is And since the body is on the surface of the earth, that will just be equal to the radius of the earth, Which is 6.371 In 2. 10 to the six what? So we can go ahead and simplify this entire expression and that gives D. Is equal to sorry, I forgot to substitute in the value for G. I'll just do that right now. So G in standardized units is equal to 6.67 Into 10 to the -11. So go ahead and evaluate this entire expression now and we'll get -1.25. Mhm. Into 10 to the seven jewels as our energy. Uh it's actually 10 to the 5th. Made a slight calculating enter. Yeah. And note that the maximum energy and there is also a factor of em over here. So I'm done. So the total energy is negative. 1.25 to 10 to the five m jules note that the maximum energy is reached when the total energy is just equal to the potential energy rather than maximum height is achieved. So we're just going to go ahead and substitute that into our formula for potential energy. And that will give us negative Mhm G M M one M two over our Yeah, no, She's just a gravitational constant. So that's 6.67 into 10. To the negative 11 M. one is simply the mass offer object. M two is the massive earth which is 5.972 into attended the 24. And our is the required height. In this case we'll go ahead and cancel out the ems and what we're left with is are being equal to you can actually cancel out the negative signs as well. So R is equal to 6.67 into 10 to the negative 11 times five point 972 into agenda 24, Divided by 1.25 into 10 to the 5th power, which gives R is equal to 3.19 into 10 to the nine meters, and that is a required answer.

Going to use conservation of energy. Initially, its speed is 10 1000 meters per second. It's a kinetic energy initial is 1/2 M V squared where V is 10 1000 meters per second. Um, potential energy initial is going to be minus G and I m over our sub e i m is going to be the mass of the earth which is 5.97 times 10 to the 24th power kilograms. Um, radius of the earth, 6.37 times 10 to the sixth power meters Kinetic energy final. It's going Teoh, Stop! So that's gonna be zero potential energy Final is negative, g um I m to what height will arise. So I think that's altitude. So h is the altitude. Um it's gonna goto our e plus h so we know everything in here. What I just need to do is solve this for H and then ah, put it into a calculator. So if I multiply by, um, you know what? I'm just gonna rearrange here a little bit. R e plus h is negative. G i m. And over 1/2 m v squared minus g I m I m over our sub e and I could have done this already. But the masses, the mess of the projectile cancels out. So now we get that age is negative. G m over 1/2 v squared minus G m over r e um, minus ari. So we can put in the numbers for that into a calculator. Um, teach negative 6.67 times 10 to the negative 11th hour times mass of the Earth, which is 5.97 times 10 to the 24th power. Okay, over 1/2 V squared. So we were given V as 10,000 when he f b squared minus d m already. Take that in. So I'm gonna copy it over R E. Radius of the earth is 6.37 times 10 to the six power meters. And then we need to subtract off radius of the earth and I get 25 point five times 10 to the sixth power in the house. Six power meters. So I guess we could write it as 25.5 mega meters


Similar Solved Questions

5 answers
(ii) Solve for z when sin(z)+cos(z) = 2i , where i = V-1.
(ii) Solve for z when sin(z)+cos(z) = 2i , where i = V-1....
5 answers
(: maraathe ceiling . This causes the 432 Ib. #eight alached t0 4 spring hanging from equilibrium There Qaring stretch 16/34 Fi on coming n sPring instuntaneous Velocity of ! the numerically cqual sa) / Linie? sssin( 6t ) 4t5 the An exemal fone- f() = 216cos(6r astem and gven an initial sirctched 7 fi below equilibrium sstem. If the spring Equalion of the: motion #` se in the upwand direction: find the Velocity of S fi Sum of the steady-state und transient terms:
(: maraa the ceiling . This causes the 432 Ib. #eight alached t0 4 spring hanging from equilibrium There Qaring stretch 16/34 Fi on coming n sPring instuntaneous Velocity of ! the numerically cqual sa) / Linie? sssin( 6t ) 4t5 the An exemal fone- f() = 216cos(6r astem and gven an initial sirctched 7...
5 answers
Given F() - f(g6)) , G(r) - g(f6)) HG) = K(r) f(x) g(+) and the following information:andFind each of the following (exact values only; no approximations):12. (a) F(3)6(2)13. (a) H(-1)K(s)fkr) - glx) 14. Find in terms of g15. A particle moves on horizontal line s0 that its position at time is given by: s(t) (2 Find the velocity and acceleration functions. Find the time(s) at which the_ particle is at rest:
Given F() - f(g6)) , G(r) - g(f6)) HG) = K(r) f(x) g(+) and the following information: and Find each of the following (exact values only; no approximations): 12. (a) F(3) 6(2) 13. (a) H(-1) K(s) fkr) - glx) 14. Find in terms of g 15. A particle moves on horizontal line s0 that its position at tim...
1 answers
LalaCatc MeFtteeneEaneaalaMe4enen
Lala Catc Me FtteeneEane aala Me4enen...
5 answers
Exercise 2.6Define A to be1 2A =1Find an elementary matrix E such that2EA =0 ~1
Exercise 2.6 Define A to be 1 2 A = 1 Find an elementary matrix E such that 2 EA = 0 ~1...
5 answers
1. The speed limit on particular interstate highways is 80 km/hr (a) What is this in meters per second? Answer: (Enter your answer to significant digits and proper units. Example: 300, 00o,000 mls is entered as (3.00E8)*m/s )(b) How many miles per hour is this? Answer: (Units are not required in this answer:)Check
1. The speed limit on particular interstate highways is 80 km/hr (a) What is this in meters per second? Answer: (Enter your answer to significant digits and proper units. Example: 300, 00o,000 mls is entered as (3.00E8)*m/s ) (b) How many miles per hour is this? Answer: (Units are not required in th...
5 answers
Find the areas of the regions bounded by the lines and curves.$y=e^{x / 2}, y=-x, x=0, x=2$
Find the areas of the regions bounded by the lines and curves. $y=e^{x / 2}, y=-x, x=0, x=2$...
5 answers
0.00 J Agrifcant IJ Question 3 sugp cornecl how should it be the number 0.000500490 written? on a calculator If this number acually has two (2) 10
0.00 J Agrifcant IJ Question 3 sugp cornecl how should it be the number 0.000500490 written? on a calculator If this number acually has two (2) 10...
5 answers
Fill in the name and empirical formula of each ionic compound that couldSome ionic compoundscationanionempirical formulaname of compoundPbPb
Fill in the name and empirical formula of each ionic compound that could Some ionic compounds cation anion empirical formula name of compound Pb Pb...
5 answers
Name the following compounds.
Name the following compounds....
5 answers
In how many different ways can a president,vice-president, secretary and treasurer be selected from a clubwith 15 members?
In how many different ways can a president, vice-president, secretary and treasurer be selected from a club with 15 members?...
5 answers
FIlI In the blank:To find the amount in an account after years with principal and an annual interest rate (in decimal form) compounded times per year, use the formula
FIlI In the blank: To find the amount in an account after years with principal and an annual interest rate (in decimal form) compounded times per year, use the formula...
5 answers
Copper(II) oxalate is only slightly soluble in water, having K,p 2.9x 10 # at 25*C. What is the solubility of CuC,Oa in water at 25"C? Present your result in units of in 8/100 mL;
Copper(II) oxalate is only slightly soluble in water, having K,p 2.9x 10 # at 25*C. What is the solubility of CuC,Oa in water at 25"C? Present your result in units of in 8/100 mL;...
5 answers
Consider cos(ze): (8 points each)Use the appropriate sum formula and the Pythagorean identity to find three ways of writing this involving cos" (0) and/or sin' "(e);Use one of these formulas t0 find an identity for sin" (0)Use one of these formulas to Iind an identity for cos (0).
Consider cos(ze): (8 points each) Use the appropriate sum formula and the Pythagorean identity to find three ways of writing this involving cos" (0) and/or sin' "(e); Use one of these formulas t0 find an identity for sin" (0) Use one of these formulas to Iind an identity for cos...
5 answers
Problem 6. (5 pts) Find a prime factorization of the following elements in Z[i] : a = 6 _ 7i, b = 90
Problem 6. (5 pts) Find a prime factorization of the following elements in Z[i] : a = 6 _ 7i, b = 90...

-- 0.022081--