1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
kaheart [24]
3 years ago
11

An object of mass m is dropped from height h above a planet of mass M and radius R .Find an expression for the object's speed as

it hits the ground.Express your answer in terms of the variables m,M,h,R and appropriate constants.v= _____

Physics
2 answers:
djyliett [7]3 years ago
8 0

An expression for the object's speed as it hits the ground is:

v = √ [ ( 2GMh ) / ( R ( R + h ) ) ]

\texttt{ }

<h3>Further explanation</h3>

Let's recall the Gravitational Force formula:

\boxed {F = G\ \frac{m_1 m_2}{R^2}}

<em>where:</em>

<em>F = Gravitational Force ( N )</em>

<em>G = Gravitational Constant ( = 6.67 × 10⁻¹¹ Nm²/kg² )</em>

<em>m = mass of object ( kg )</em>

<em>R = distance between object ( m )</em>

Let us now tackle the problem!

\texttt{ }

<u>Given:</u>

mass of object = m

height position of object = h

mass of planet = M

radius of planet = R

initial speed of object = u = 0 m/s

<u>Asked:</u>

final speed of object = v = ?

<u>Solution:</u>

<em>We will calculate the object's speed by using </em><em>Conservation of Energy </em><em>formula as follows:</em>

Ep_1 + Ek_1 = Ep_2 + Ek_2

-G \frac{Mm}{R + h} + \frac{1}{2}m u^2 = -G \frac{Mm}{R} + \frac{1}{2}m v^2

-G \frac{Mm}{R + h} + \frac{1}{2}m (0)^2 = -G \frac{Mm}{R} + \frac{1}{2}m v^2

-G \frac{Mm}{R + h} = -G \frac{Mm}{R} + \frac{1}{2}m v^2

G \frac{Mm}{R} -G \frac{Mm}{R + h} = \frac{1}{2}m v^2

G \frac{M}{R} -G \frac{M}{R + h} = \frac{1}{2} v^2

v^2 = 2GM ( \frac{1}{R} -\frac{1}{R + h} )

v^2 = 2GM\frac{h}{R(R +h) }

\boxed {v = \sqrt { \frac{ 2GMh } { R(R +h) } } }

\texttt{ }

<h3>Learn more</h3>
  • Unit of G : brainly.com/question/1724648
  • Velocity of Runner : brainly.com/question/3813437
  • Kinetic Energy : brainly.com/question/692781
  • Acceleration : brainly.com/question/2283922
  • The Speed of Car : brainly.com/question/568302

\texttt{ }

<h3>Answer details</h3>

Grade: High School

Subject: Mathematics

Chapter: Gravitational Force

Thepotemich [5.8K]3 years ago
4 0

Answer:

Explanation:

Assuming that h is much smaller than R, then we can say the acceleration of gravity is approximately constant.

Potential energy = Kinetic energy

mgh = 1/2 mv²

v = √(2gh)

v = √(2 (MG/R²) h)

v = √(2 MGh) / R

You might be interested in
What are the types of realistic fiction?.
Daniel [21]

The types of realistic fiction:<u> are </u><u>historical </u><u>and </u><u>contemporary </u><u>fiction.</u>

Practical fiction creates imaginary characters and conditions that depict our world and society. It focuses on themes of growing up and confronting non-public and social problems. This genre portrays characters coming to apprehend themselves and others.

Realistic Fiction is divided into two elements: ancient and modern-day fiction. ancient fiction takes place in a time far-flung enough to be taken into consideration records, as opposed to contemporary fiction which takes vicinity these days or within the recent beyond. sensible fiction is a style of testimonies in which the events are made up, but they may easily occur in actual existence. those styles of stories take place in acquainted, ordinary settings and have normal characters.

Learn more about Realistic Fiction here:

brainly.com/question/14596007

#SPJ4

8 0
1 year ago
You need to remove a broken light bulb from a lamp. without a pair of gloves, you are likely to cut yourself on the jagged glass
mojhsa [17]
<span>You have just demonstrated an insight learning. Internal insight occurs if one learned a new way without the help of environmental factors. In here, what the person initially learned that if one saw a broken light bulb from a lamp, he can be cut through the jagged glass if one does not wear a pair of gloves. And maybe because at the moment, the person could not find one, he felt using a cut potato to pick up the pieces of the broken lamp. This is a demonstration of insight learning. The person found a way to pick up the pieces of the broken lamp by using his instinct at the moment. The person is not influenced by an outside source to tell him to use a potato. </span>
5 0
3 years ago
A.complete the following sentences with your own result or condition
ludmilkaskok [199]

1. If I hadn't bought that car yesterday.

2. I would have never bought the tickets for today..

3. She wouldn't have gotten suspended.

4. We could've worked on our project.

5. but I was in the shower.

6 0
3 years ago
The main difference between internal combustion engine and the diesel engine is?
Sav [38]
<span>The difference between a internal combustion engine and a diesel engine is the ignition, But a Diesel engine is an internal combustion engine. The both burn internal one uses compression to fire the other uses ignition system.</span>
8 0
3 years ago
Read 2 more answers
How many turns are in its secondary coil, if its input voltage is 120 V and the primary coil has 210 turns
Tasya [4]

Complete Question

How many turns are in its secondary coil, if its input voltage is 120 V and the primary coil has 210 turns.

The output from the secondary coil is  12 V

Answer:

The value  is  N_s  =  21 \  turns

Explanation:

From the equation we are told that

   The input voltage is  V_{in}  = 120 \ V

   The number of turns of the primary coil is N_p =  210 \  turn

    The output from the secondary is V_o =  12V

From the transformer equation

   \frac{N_p}{V_{in}}  =\frac{N_s}{V_o}

Here N_s is the number of turns in the secondary coil

=> N_s  =  \frac{N_p}{V_{in}}  *  V_s

=>N_s  =  \frac{210}{120}  *  12

=>N_s  =  21 \  turns

4 0
3 years ago
Other questions:
  • Which part of the electromagnetic spectrum generally gives us our best views of stars forming in dusty clouds?
    9·1 answer
  • What is the lowest frequency that will resonate in an organ pipe 2.00 m in length, closed at one end? The speed of sound in air
    15·1 answer
  • A rock is dropped from the ceiling of a truck's cargo bay. with the truck moving at constant velocity, the rock strikes the floo
    5·1 answer
  • During a test a rocket travels upward at 90 m/s , and when it is 50 m from the ground its engine fails. Determine the maximum he
    6·2 answers
  • What is the frequency of a radio wave of wavelength 150 m if the velocity of radio waves in free space is 3 × 10^8 m s–¹ ?​
    13·1 answer
  • Select the correct answer. In a given chemical reaction, the energy of the products is greater than the energy of the reactants.
    5·1 answer
  • An artificial satellite orbits Earth at a speed of 7800 m/s and a height of 200 km above Earth’s surface. The satellite experien
    7·1 answer
  • Write a short story (3 - 5 sentences) that describes a situation with the motion experiences in this graph. Please Help Me.
    10·1 answer
  • A spring of negligible mass and force constant k = 430 N/m is hung vertically, and a 0.270 kg pan is suspended from its lower en
    14·1 answer
  • A car starting from rest accelerates uniformly at 3
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!