Question

A satellite that is spinning clockwise has four low-mass solar panels sticking out as shown; the mass of the satellite is 800 kg. A tiny meteor of mass 5 kg traveling at high speed rips through one of the solar panels and continues in the same direction but at reduced speed. In the figure v1 = 900 m/s and v2 = 440 m/s are the initial and final speeds of the meteor, and v = 15 m/s is the initial speed of the satellite in the x direction. The angle θ = 26°, h = 2 m, and R = 1.4 m. Calculate the final velocity of the center of mass of the satellite:

Answer 1

Answer:

final velocity of center of mass of satellite is 17.63 m/s at 4.1 degree

Explanation:

here in this situation we can use momentum conservation in x direction as well as in Y direction

So first we will apply in x direction

$m_1v_{1x} + m_2v_2 = m_1v_{1xf} + m_2v_{2fx}$

$5(900)cos26 + 800(15) = 5(440)cos26 + 800 v_{2fx}$

$v_{2fx} = 17.58 m/s$

Now by momentum conservation in Y direction

$m_1v_{1y} + m_2v_2 = m_1v_{1yf} + m_2v_{2fy}$

$5(900)sin26 + 800(0) = 5(440)sin26 + 800 v_{2fy}$

$v_{2fy} = 1.26 m/s$

Now the net speed of center of mass of the satellite is given as

$v = \sqrt{v_{2fx}^2 + v_{2fy}^2}$

$v = 17.63 m/s$

direction is given as

$\theta = tan^{-1}\frac{v_{2fy}}{v_{2fx}}$

$\theta = tan^{-1}\frac{1.26}{17.58} = 4.1 degree$

Answer 2

We are given with
ms = 800 kg
mm = 5 kg
v1 = 900 m/s
v2 = 440 m/s
v = 15 m/s
θ = 26°
h = 2 m
R = 1.4 m

To calculate the final velocity of the center of mass of the satellite, we need to use the law of conservation of momentum
ms v1 + mm v2 = ms' v1' + mm v2'
The velocity that will be used will the x component which is
vx = v cos θ
Substitute the given values and solve for v1'