Answer:
r = 41.1 10⁹ m
Explanation:
For this exercise we use the equilibrium condition, that is, we look for the point where the forces are equal
∑ F = 0
F (Earth- probe) - F (Mars- probe) = 0
F (Earth- probe) = F (Mars- probe)
Let's use the equation of universal grace, let's measure the distance from the earth, to have a reference system
the distance from Earth to the probe is R (Earth-probe) = r
the distance from Mars to the probe is R (Mars -probe) = D - r
where D is the distance between Earth and Mars
M_earth (D-r)² = M_Mars r²
(D-r) = 
r
r ( 
) = D
r = 
We look for the values in tables
D = 54.6 10⁹ m (minimum)
M_earth = 5.98 10²⁴ kg
M_Marte = 6.42 10²³ kg = 0.642 10²⁴ kg
let's calculate
r = 54.6 10⁹ / (1 + √(0.642/5.98) )
r = 41.1 10⁹ m
Answer:
a) It is moving at 
when reaches the ground.
b) It is moving at 
when reaches the ground.
Explanation:
Work energy theorem states that the total work on a body is equal its change in kinetic energy, this is:
(1)
with W the total work, Ki the initial kinetic energy and Kf the final kinetic energy. Kinetic energy is defined as:
(2)
with m the mass and v the velocity.
Using (2) on (1):
(3)
In both cases the total work while the objects are in the air is the work gravity field does on them. Work is force times the displacement, so in our case is weight (w=mg) of the object times displacement (d):
(4)
Using (4) on (3):
(5)
That's the equation we're going to use on a) and b).
a) Because the branch started form rest initial velocity (vi) is equal zero, using this and solving (5) for final velocity:
b) In this case the final velocity of the boulder is instantly zero when it reaches its maximum height, another important thing to note is that in this case work is negative because weight is opposing boulder movement, so we should use -mgd:
Solving for initial velocity (when the boulder left the volcano):
$0.60
90 mins is 1.5 hrs
5 kW × 1.5 = 7.5 kWh
7.5 kWh × $0.08 = $0.60
Answer:
The magnitude of the angular acceleration is 
Explanation:
From the question we are told that
The angular speed of CD is 
time taken to decelerate is 
The final angular speed is 
The angular acceleration is mathematically represented as
substituting values
The negative sign show that the CD is decelerating but the magnitude is
