
Explanation:
First we need to find the acceleration due to gravity on the planet. The wrench took 0.809 s to fall from a height of 4.50 m so we can use the equation

Solving for g, we get

Recall that the acceleration due to gravity on a planet's surface can be written as

We can express the mass of the planet
in terms of its density
as follows:

The expression for g then becomes

Solving for
we get

![\:\:\:\:\:\:\:= \left[\dfrac{3(13.8\:\text{m/s}^2)}{4\pi (6.674×10^{-11}\:\text{Nm}^2\text{/kg}^2)(5500\:\text{kg/m}^3)}\right]](https://tex.z-dn.net/?f=%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%3D%20%5Cleft%5B%5Cdfrac%7B3%2813.8%5C%3A%5Ctext%7Bm%2Fs%7D%5E2%29%7D%7B4%5Cpi%20%286.674%C3%9710%5E%7B-11%7D%5C%3A%5Ctext%7BNm%7D%5E2%5Ctext%7B%2Fkg%7D%5E2%29%285500%5C%3A%5Ctext%7Bkg%2Fm%7D%5E3%29%7D%5Cright%5D)

Answer:
I don't know I'm sorry I will tell you another answer asks me
Answer:
Explanation:
We are basically needing to solve for the time in the equation d = rt, where d is the distance around Mars (aka the circumference), r is the velocity, and t is time. We need to find the circumference and the velocity. We will begin with the velocity.
Because the gravitational attraction between Phobos and Mars provides the centripetal acceleration necessary to keep Phobos in its (sort of) circular path, the equation we use for this is:
which says that Force supplied by gravity is equal to the centripetal force. Expanding that:

When we move that around mathematically to solve for the velocity value, what we end up with is:
and filling in:
and we get that
v = 2100 m/s
Now for the circumference:
C = 2πr and
C = 2(3.1415)(9.38 × 10⁶) so
C = 5.9 × 10⁷
Putting that all together in the C = vT equation:
5.9 × 10⁷ = 2100T so
T = 2.8 × 10⁴ sec or 7.8 hours
The characteristics of the scalar product allows to find the angle between the two vectors is:
The scalar product is the product between two vectors whose result is a scalar.
A . B = |A| |B| cos θ
Where A and B are the vectors, |A| and |B| are the modules of the vectors and θ at the angle between them.
The vector is given in Cartesian coordinates and the unit vectors in these coordinates are perpendicular.
i.i = j.j = 1
i.j = 0
A . B = (4 i - 4j). * -5 i + 7j)
A . B = - 4 5 - 4 7
A. B = -48
We look for the modulus of each vector.
|A| =
|A| =
|A| = 4 √2
|B| =
|B| = 8.60
We substitute.
-48 = 4√2 8.60 cos θ
-48 = 48.66 cos θ
θ = cos⁻¹
θ = 170º
In conclusion using the dot product we can find the angle between the two vectors is:
Learn more about the scalar product here: brainly.com/question/1550649