Ok...I figured out part a but I am having trouble with b. part a was:
Zero, a hypothetical planet, has a mass of 1.0x10^23 kg, a radius of 3.0x10^6 m, and no atmosphere. A 10 kg space probe is to be launched vertically from its surface.
(a) If the probe is launched with an initial kinetic energy of 5.0x10^7 J, what will be its kinetic energy when it is 4.0x10^6 m from the center of Zero?
so I did KE + U = constant,
V = sqrt(2GM/R)
V = sqrt(2(6.67e-11)(1.0e23)/(3.0e6))
V = 2108.7
(1/2) mV^2 - GMm/R = constant
(.5(10)(2108.7)^2 - ((6.67e-11)(1.0e23)(10)/(4.0e6))
111165392.3 - 16675000 = 94490392.3 = 9.4e7=constant
9.4e7-5e7=4.4e7 J which is the right answer...but for b:
If the probe is to achieve a maximum distance of 8.0x10^6 m from the center of Zero, with what initial kinetic energy must it be launched from the surface of Zero?
->I am not sure what to do. I recalculated the constant using the radius of 8e6 m and got 2.78e6 J but then I am not sure what to use for U. U=mgd so I tried U=(10)(9.8)(3e6) and subtracted that from 2.78e6 J but that is wrong. What am I missing?

Potential energy is not M g d in an inverse-square-law gravitational field. It is -MmG/r = -MmG/R^2 * R^2/r
= -m g'R^2/r
where g' is the acceleration of gravity at the planet's surface, M is the planet's mass, and R is the planet's radius. m is the mass of the probe and r is the distance of the probe from the center of the planet. That is probably where you made your mistake

  1. 👍 0
  2. 👎 0
  3. 👁 110
  1. my book has Mass=5.0 X 10^(23)

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. Stats - Post Hoc Analysis

    This is a question I am working on. i have successfully figured out part A and am having trouble with part B. (My work for Part B is shown below) ______________________________________ Two new therapies designed to increase levels

    asked by VC15 on June 17, 2006
  2. Algebra help please

    Part A: Divide (16x^5y^4 + 6x^3y - 2x^2y - 24x^2y^4) by -2x^2y. Part B: How would your answer in Part A be affected if the x2 variable in the denominator was just an x? Part C: What is the degree and classification of the

    asked by Andrea on March 18, 2015
  3. Chemistry

    CS2(g) + O2(g) CO2(g) + SO2(g) (a) Consider the unbalanced equation above. What is the maximum mass of SO2 that can be produced when 46.0 g of CS2 and 29.0 g O2 react? (b) Assume the reaction in part (a) goes to completion.

    asked by Tiffany on February 28, 2010
  4. VB

    I am new here; say to everyone first. Here is the a question for coding list box; it has two part: first part: Create a project that stores personal information for a little electronic "black book"; the fields in the file should

    asked by austin on November 16, 2011
  5. physics

    A light spring having a force constant of 130N/m is used to pull a 7.50kg sled on a horizontal frictionless ice rink. The sled has an acceleration of 2.50m/s^2? Part A: By how much does the spring stretch if it pulls on the sled

    asked by lori on September 26, 2013
  6. World History A

    The earliest societies of Mesopotamia believed their rulers had divine right (1). As these societies grew in size, more complex governments and bureaucracies emerged (2). As a result, ancient Mesopotamia became the birthplace of a

    asked by DeafeninGaming on November 5, 2017
  7. chem

    I got through the first part easily, got -352.9kJ Having trouble with the second part "The meals-ready-to-eat (MREs) in the military can be heated on a flameless heater. The source of energy in the heater is shown below. Mg(s) + 2

    asked by Anonymous on November 20, 2010
  8. AP AB Calculus

    Linear approximation: Consider the curve defined by -8x^2 + 5xy + y^3 = -149 a. find dy/dx b. write an equation for the tangent line to the curve at the point (4,-1) c. There is a number k so that the point (4.2,k) is on the

    asked by Katie G on December 17, 2014
  9. Physics-Gravitation

    What is the gravitational potential energy of a two-particle system with masses 5.4 kg and 5.0 kg, if they are separated by 1.3 m? If you triple the separation between the particles, how much work is done (b) by the gravitational

    asked by Jessica on January 2, 2011
  10. Check Please(Math)

    (-2x^2y)^3*(5xy^3)^2=(-2x^2y)^3 = -8 x^6 y^3 *Please check my work. What did you do with the (5xy^3)^2 part. The first part you did ok. But you can't just throw away part of the equation. I don't get that part.What do I do there.?

    asked by Margie on February 6, 2007
  11. AP English

    I'm having trouble finding IRONIES in George Orwell's "1984" book in PART 3 where it starts off from page 186 till the end. The beginning of part 3 goes " He did not know where he was... and so on". Some books are numbered

    asked by Ally on September 8, 2016

More Similar Questions