Answer:
1.38*10^18 kg
Explanation:
According to the Newton's law of universal gravitation:

where:
G= Gravitational constant (6.674×10−11 N · (m/kg)2)
ma= mass of the astronaut
mp= mass of the planet

so:

Answer:
4.6×10^-7 m or 0.46nm
Explanation:
From
Wo= hc/λ
Where:
Wo= work function of the metal
h= planks constant
c= speed of light
λ= wavelength
λ= hc/Wo
λ= 6.6×10^-34 × 3×10^8/4.30×10^-19
λ= 4.6×10^-7 m
If no other forces act on the object, according to Newton’s first law, the spacecraft will continue moving at a constant velocity, assuming that a planet or something with large mass doesn’t cross its path. Forces are not required to continue the motion of an object on a frictionless plane at a constant rate.
Answer:
i = 0.477 10⁴ B
the current flows in the counterclockwise
Explanation:
For this exercise let's use the Ampere law
∫ B . ds = μ₀ I
Where the path is closed
Let's start by locating the current vines that are parallel to the z-axis, so it must be exterminated along the x-axis and as the specific direction is not indicated, suppose it extends along the y-axis.
From BiotSavart's law, the field must be perpendicular to the direction of the current, so the magnetic field must go in the x direction.
We apply the law of Ampere the segment parallel to the x-axis is the one that contributes to the integral, since the other two have an angle of 90º with the magnetic field
Segment on the y axis
L₀ = (y2-y1)
L₀ = 3-0 = 3 cm
Segment on the point x = 2 cm
L₁ = 3-0
L₁ = 3cm
B L = μ₀ I
B 2L = μ₀ I
i = 2 L B /μ₀
i= 2 0.03 / 4π 10⁻⁷ B
i = 4.77 10⁴ B
The current is perpendicular to the magnetic field whereby the current flows in the counterclockwise
The kinetic energy of an object of mass m and velocity v is given by

Let's call

the initial speed of the car, so that its initial kinetic energy is

where m is the mass of the car.
The problem says that the car speeds up until its velocity is twice the original one, so

and by using the new velocity we can calculate the final kinetic energy of the car

so, if the velocity of the car is doubled, the new kinetic energy is 4 times the initial kinetic energy.