Answer:
(a) The Work need to place spacecraft into low orbit is
(b) Additional Work need to place the spacecraft far away from the earth is
.
(c) From part(a) and part(b) we observe the Both quantities are equal.
Explanation:
Explanation is in the following attachments
Explanation:
Given that,
Mass of the shopping cart, 
Initial speed of the shopping cart, 
Mass of the box, 
Initial speed of the box,
(at rest)
They stick together and continue moving at a new velocity. It is a case of inelastic collision.
(a) The momentum of the shopping cart before the collision is given by :

(b) The momentum of the box before the collision is given by :

(c) The velocity of the combined shopping cart/box wreckage after the collision is given by using the conservation of momentum as :

Hence, this is the required solution.
When an object falls or is dropped from rest it's initial velocity is zero.
Using the equations for a motion in straight line. I can find the time it takes to reach 3.0 m down (half way).
x = vt - 4.9t²
-3 = 0 - 4.9t²
-3/-4.9 = t²
0.6122 = t²
0.7825 sec = t
v = v - gt
v = 0 - 9.8(0.7825)
v = -7.67 m/s
the negative denotes downward direction.
You could also solve the problem using potential and kinetic energy.
Since it starts with maximum PE and gets converted to KE when it hits the ground. mgh = mv²/2
mass cancels, use 3 meters for the halfway distance
-9.8(-3) = v²/2
29.4 * 2 = v²
√(58.8) = 7.67 m/s downwards
The mass of the planet Gallifrey is 8 times the mass of the Earth.
- let the gravitational field of Earth = g
- let the radius of the Earth = R
- gravitational field of Gallifrey = 2g
- radius of Gallifrey = 2R
<h3>What is gravitational potential energy?</h3>
- This is the work done in moving an object to a certain distance against gravitational field.
The gravitational field strength of the Earth is given as follows;

The gravitational field strength of the Planet Gallifrey is calculated as follows;


Thus, the mass of the planet Gallifrey is 8 times the mass of the Earth.
Learn more about gravitational field strength here: brainly.com/question/14080810
Answer:
GE = ME -
, which agrees with option C in your list.
Explanation:
The definition of Mechanical Energy (ME) of a system is the addition of the gravitational potential energy (GE) plus the kinetic energy (KE) of the system:
ME = GE + KE
Given that the KE is:
,
solving for GE in the formula above gives:
GE = ME - KE = ME -
, which agrees with option C