Please answer each question with step by step answers so I understand the solutions. Thanks!

1. A space probe is in deep space far beyond the edge of the solar system when it uses up all its nuclear fuel. What is true?
(a) The space probe will immediatly come to a stop
(b) The space probe will very slowly come to a stop
(c) The space probe will continue moving at the same speed
(d) The space probe will speed up

2. A rocket explodes in mid-air. Which is true during the explosion?
(a) Only mechanical energy is conserved
(b) Only momentum is conserved
(c) Both mechanical energy and momentum are conserved
(d) Neither mechanical energy nor momentum are conserved

3. A girl of mass M is on a turning Ferris wheel of radius R. She moves at constant speed v. What is the magnitude of the change of her momentum between when she is at the top and bottom of the Ferris wheel.
(a) 0
(b) Mv
(c) 2Mv
(d) MgR
(e) 2MgR

(FOR DIAGRAM PLEASE SEE ATTACHMENT)

4. A sheet of copper of uniform thickness is shaped like a triangle with a hole cut out of one corner. Mark the approximate location of the center of the mass.

A 5.0 x 104 kg spaceprobe is traveling at a speed of 11000 m/s through deep space. Retrorockets are fired along the line of motion to reduce the probe/s speed. The retrorockets generate a force of 4.0 x 10^5 N over a distance of 2500 km. What is the final speed of the probe?

At t=0, the wavefunction of a free particle is:
psi(x,0) = {(sqrt b/2*pi)sin(bx) for |x|<((2*pi)/b)
{0 for |x|> or = ((2*pi)/b))
a) What is the probability of finding the particle in the interval 0 less than or equal to x less than or equal to pi/2b?
b) What is the momentum am

"A 122 kg astronaut (including space suit) acquires a speed of 2.50 m/s by pushing off with his legs from a 1900 kg space capsule. What is the change in speed of the capsule?"

A 82 kg astronaut is space-walking outside the space capsule and is stationary when the tether line breaks. As a means of returning to the capsule, he throws his 3.1 kg wrench at a speed of 13 m/s away from the capsule. At what speed does the astronaut move toward the capsule?

We study the relationship between the position space wave function and the momentumspace wave function in quantum mechanics. We show that they are related by the Fourier transform, more specifically we show that a momentum wave function given by the Fourier transform of the space wave function satisfies the requirements to be a

At its closest approach, Mars is 56 million km from Earth. How long would it take to send a radio message from a spaceprobe of Mars to earth when the planets are at this closest distance?

The hydrogen atom ground state may be described by the spatial wave function as:
phi(r)= [(1/(Pi*(a_0^(3)))^(1/2)]*e^(-r/a0)
This is where a_0 is the Bohr radius. Using the following equation, please calculate the momentum wave function.
integral[(e^(-a*r + i*b*r))*(d^(3))*(r) = 8*Pi*a/((a^(2) + b^(2))^(2))
See the at

An object of mass 2 kg travelling in a straight line with a velocity of 20m/sec collides with, and strikes to, a stationary object of mass 3 kg. They both move off together in the same straight line with a velocity of v m/sec. If no external forces are acting calculate
a. the total momentum just before the impact
b. the tot