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
horsena [70]
3 years ago
12

A team of astronauts is on a mission to land on and explore a large asteroid. In addition to collecting samples and performing e

xperiments, one of their tasks is to demonstrate the concept of the escape speed by throwing rocks straight up at various initial speeds. With what minimum initial speed ????esc will the rocks need to be thrown in order for them never to "fall" back to the asteroid? Assume that the asteroid is approximately spherical, with an average density ????=4.49×106 g/m3 and volume ????=3.32×1012 m3 . Recall that the universal gravitational constant is ????=6.67×10−11 N·m2/kg2 .
Physics
1 answer:
GenaCL600 [577]3 years ago
3 0

Answer:

463.4 m/s

Explanation:

The escape velocity on the surface of a planet/asteroid is given by

v=\sqrt{\frac{2GM}{R}} (1)

where

G is the gravitational constant

M is the mass of the planet/asteroid

R is the radius of the planet/asteroid

For the asteroid in this problem, we know

\rho=4.49\cdot 10^6 g/m^3 is the density

V=3.32\cdot 10^{12} m^3 is the volume

So we can find its mass:

M=\frac{\rho}{V}=(4.49\cdot 10^6 g/m^3)(3.32\cdot 10^{12}m^3)=1.49\cdot 10^{19} kg

Also, the asteroid is approximately spherical, so its volume is given by

V=\frac{4}{3}\pi R^3

where R is the radius. Solving the formula for R, we find its radius:

R=\sqrt[3]{\frac{3V}{4\pi}}=\sqrt[3]{\frac{3(3.32\cdot 10^{12}m^3)}{4\pi}}=9256 m

So now we can use eq.(1) to find the escape velocity:

v=\sqrt{\frac{2(6.67\cdot 10^{-11})(1.49\cdot 10^{19}kg)}{9256 m}}=463.4 m/s

You might be interested in
A simple pendulum, 1.00 m in length, is released from rest when the support string is at an angle of 35.0 from the vertical. Wh
taurus [48]

Answer:

Explanation:

Length = 1.00 m

If the length is 1.0, the vertical distance pivot to bob is cos 35 = 0.819

At the lowest point, vertical distance is 1.0, so the change is the difference, 0.181 meter

The potential energy of that height is converted to kinetic energy of motion, which determines the speed.

PE = KE

mgh = ½mV²

V = √(2gh) = 1.88 m/s

7 0
3 years ago
A sample of an ideal gas initially occupies a volume of 6 L. The pressure of the sample is then doubled while it is cooled to on
Troyanec [42]

Answer:

V₂= 1 L

Explanation:

Given that

Volume occupies V₁= 6 L

Initial pressure = P₁

Initial temperature = T₁

The final pressure =P₂ = 2 P₁

Final volume =V₂

Final temperature = T₁/3

As we know that equation for ideal gas

P V = m R T

P=pressure,  V=volume,   T=temperature

m=mass  ,R=gas constant

Now from mass conservation

m=\dfrac{P_1V_1}{RT_1}=\dfrac{P_2V_2}{RT_2}

\dfrac{P_1V_1}{RT_1}=\dfrac{P_2V_2}{RT_2}

\dfrac{P_1\times 6}{RT_1}=3\times \dfrac{2P_1V_2}{RT_1}

6 = 3 x 2 V₂

V₂= 1 L

So the final volume will be 1 L

4 0
3 years ago
Why are water storage tanks usually placed on high towers
sammy [17]
Thay are on high towers because if it was below how would the water flow. Putting it on high towers gives you an advantage of the gravity with means you got free pressure without having to use a pump.

<span>Water pressure = Height * density * gravity</span>
7 0
3 years ago
Read 2 more answers
A jet is travelling at a speed of 1200 km/h and drops cargo from a height of 2.5 km above the ground Calculate the time it takes
OLEGan [10]

a) Time of flight: 22.6 s

To calculate the time it takes for the cargo to reach the ground, we just consider the vertical motion of the cargo.

The vertical position at time t is given by

y(t) = h +u_y t - \frac{1}{2}gt^2

where

h = 2.5 km = 2500 m is the initial height

u_y = 0 is the initial vertical velocity of the cargo

g = 9.8 m/s^2 is the acceleration of gravity

The cargo reaches the ground when

y(t) = 0

So substituting it into the equation and solving for t, we find the time of flight of the cargo:

0 = h - \frac{1}{2}gt^2\\t=\sqrt{\frac{2h}{g}}=\sqrt{\frac{2(2500)}{9.8}}=22.6 s

b) 7.5 km

The range travelled by the cargo can be calculated by considering its horizontal motion only. In fact, the horizontal motion is a uniform motion, with constant velocity equal to the initial velocity of the jet:

v_x = 1200 km/h \cdot \frac{1000 m/km}{3600 s/h}=333.3 m/s

So the horizontal distance travelled is

d=v_x t

And if we substitute the time of flight,

t = 22.6 s

We find the range of the cargo:

d=(333.3)(22.6)=7533 m = 7.5 km

7 0
3 years ago
Neutron stars are extremely dense objects that are formed from the remnants of supernova explosions. Many rotate very rapidly. S
Alja [10]

Answer:

16294 rad/s

Explanation:

Given that

M(ns) = 2M(s), where

M(s) = 1.99*10^30 kg, so that

M(ns) = 3.98*10^30 kg

Again, R(ns) = 10 km

Using the law of gravitation, the force between the Neutron star and the sun is..

F = G.M(ns).M(s) / R²(ns), where

G = 6.67*10^-11, gravitational constant

Again, centripetal force of the neutron star is given as

F = M(ns).v² / R(ns)

Recall that v = wR(ns), so that

F = M(s).w².R(ns)

For a circular motion, it's been established that the centripetal force is equal to the gravitational force, hence

F = F

G.M(ns).M(s) / R²(ns) = M(s).w².R(ns)

Making W subject of formula, we have

w = √[{G.M(ns).M(s) / R²(ns)} / {M(s).R(ns)}]

w = √[{G.M(ns)} / {R³(ns)}]

w = √[(6.67*10^-11 * 3.98*10^30) / 10000³]

w = √[2.655*10^20 / 1*10^12]

w = √(2.655*10^8)

w = 16294 rad/s

7 0
3 years ago
Other questions:
  • A 100.0 mL sample of 1.020 M HCl is mixed with a 50.0 mL sample of 2.040 M NaOH in a Styrofoam cup. If both solutions were initi
    7·1 answer
  • A fancart of mass 0.8 kg initially has a velocity of &lt; 0.8, 0, 0 &gt; m/s. Then the fan is turned on, and the air exerts a co
    9·1 answer
  • A cart loaded with bricks has a total mass of 25.1 kg and is pulled at constant speed by a rope. The rope is inclined at 21.3 ◦
    15·1 answer
  • 1. Which of the following is the broadest, most inclusive taxonomic group? genus species family domain 2. The species name of th
    9·1 answer
  • If Teresa's daughter is my daughters mother who am I to Teresa?
    9·2 answers
  • Physical science question please help
    11·1 answer
  • "For an object moving at a constant speed, we would expect to see a position graph with a
    15·1 answer
  • How does a rubber rod become negatively charged through friction?
    13·1 answer
  • A plane took 3.55 hours to finish a journey. If the distance of
    13·1 answer
  • How to solve projectile motion problems with angles.
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!