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ipn [44]
3 years ago
7

The concept of critical density is just like the idea of escape velocity for a projectile launched from the earth. An object lau

nched with a velocity less than the escape velocity will fall back to the earth, and an object launched with one greater than the escape velocity can escape the earth's gravitational field. Find an expression for vesc, the escape velocity of a projectile launched from the earth's surface. Express your answer in terms of the universal gravitational constant G, the mass of the earth Me, and the radius of the earth Re.
Physics
1 answer:
ikadub [295]3 years ago
5 0

Answer:

v = √ 2 G M/ R_{e}

Explanation:

To find the escape velocity we can use the concept of mechanical energy, where the initial point is the surface of the earth and the end point is at the maximum distance from the projectile to the Earth.

Initial

        Em₀ = K + U₀

Final

        Em_{f} =  U_{f}

The kinetic energy is k = ½ m v²

The gravitational potential energy is U = - G m M / r

r is the distance measured from the center of the Earth

How energy is conserved

       Em₀ =  Em_{f}

       ½ mv² - GmM / R_{e} = -GmM / r

       v² = 2 G M (1 /  R_{e} – 1 / r)

       v = √ 2GM (1 / R_{e} – 1 / r)

The escape velocity is that necessary to take the rocket to an infinite distance (r = ∞), whereby 1 /∞ = 0

        v = √ 2GM /  R_{e}

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vA child is in danger of drowning in the Merimac river. The Merimac river has a current of 3.1 km/hr to the east. The child is 0
ikadub [295]

Answer:

d = 2.26 km

Explanation:

Let the child is moving with speed same as the speed of water flow

So here the position of child with respect to flow must be zero

And if the boat start at an angle with the vertical

so its relative speed with flow of water is given as

v_x = 24.8 sin\theta

v_y = 24.8 cos\theta

now the time to reach the child is given as

\frac{0.6}{24.8 cos\theta} = \frac{2.5}{24.8 sin\theta }

so now we have

\theta = 76.5 degree

So the time to catch the child is given as

t = \frac{0.6}{24.8 cos78.2}

t = 0.104 h

So distance moved by it in 0.104 h

distance moved by the boat in upstream direction given as

x = (24.8 sin 74.8 - 3.1)(0.104)

x = 2.18 km

In y direction the displacement of boat is

y = 0.6 km

net displacement of the ball is given as

d = \sqrt{x^2 + y^2}

d = \sqrt{2.18^2 + 0.6^2}

d = 2.26 km

4 0
3 years ago
a 3520 kg truck moving north at 18.5 m/s makes an INELASTIC collision with an 1480 kg car moving east after colliding they have
anyanavicka [17]

Answer:

Explanation:

An inelastic collision is one where 2 masses collide and stick together, moving as a single mass after the collision occurs. When we talk about this type of momentum conservation, the momentum is conserved always, but the kinetic momentum is not (the velocity changes when they collide). Because there is direction involved here, we use vector addition. The picture before the collision has the truck at a mass of 3520 kg moving north at a velocity of 18.5. The truck's momentum, then, is 3520(18.5) = 65100 kgm/s; coming at this truck is a car of mass 1480 kg traveling east at an unknown velocity. The car's momentum, then, is 1480v. The resulting vector (found when you pick up the car vector and stick the initial end of it to the terminal end of the truck's momentum vector) forms the hypotenuse of a right triangle where one leg is 65100 kgm/s, and the other leg is 1480v. Since we already know the final velocity of the 2 masses after the collision, we can use that to find the final momentum, which will serve as the resultant momentum vector in our equation (we'll get there in a sec). The final momentum of this collision is

p = mv and

p = (3520 + 1480)(13.6) so

p = 68000. Final momentum. The equation for this is a take-off of Pythagorean's Theorem and the one used to find the final magnitude of a resultant vector when you first began your vector math in physics. The equation is

p_f=\sqrt{(p_{truck})^2+(p_{car})^2} which, in words, is

the final momentum after the collision is equal to the square root of the truck's momentum squared plus the car's momentum squared. Filling in:

68000=\sqrt{(65100)^2+(1480v)^2} and

(68000)^2=(65100)^2+(1480v)^2 and

4624000000=4238010000+2190400v^2  and

385990000=2190400v^2 and

176.2189554=v^2 so

v = 13.3 m/s at 72.6°

6 0
3 years ago
This is my question. I need the answer stat.
Kipish [7]

Answer:

Explanatioyour answers look right, but if there has , has to be another answer its a , but your answers are right

5 0
2 years ago
Read 2 more answers
Which statement is correct? Theories are accepted as true when a single experiment yields similar results to another one. When a
levacccp [35]
The third statement is correct.

3 0
2 years ago
Read 2 more answers
An object is 2.0 m in front of a plane mirror. Its image is:?
maria [59]
Planes don’t have mirrors
6 0
3 years ago
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