Answer: Around 364 to 480
Answer: 8 years
Explanation:
According to Kepler’s Third Law of Planetary motion <em>“The square of the orbital period of a planet is proportional to the cube of the semi-major axis (size) of its orbit”:</em>
<em />
(1)
In other words: this law states a relation between the orbital period of a body (moon, planet, satellite, comet, asteroid) orbiting a greater body in space (the Sun, for example) with the size of its orbit.
However, if is measured in years (Earth years), and is measured in astronomical units (equivalent to the distance between the Sun and the Earth: ), equation (1) becomes:
(2)
This means that now both sides of the equation are equal.
Knowing and isolating from (2):
(3)
(4)
Finally:
This is the period of the asteroid
Answer:
20.1 m
Explanation:
First, find the time it takes for the cannonball to travel the horizontal distance of 50.0 m.
Given (in the x direction):
Δx = 50.0 m
v₀ = 68 cos 25° m/s
a = 0 m/s²
Find: t
Δx = v₀ t + ½ at²
(50.0 m) = (68 cos 25° m/s) t + ½ (0 m/s²) t²
t = 0.811 s
Now find the vertical displacement after that time.
Given (in the y direction):
v₀ = 68 sin 25° m/s
a = -9.8 m/s²
t = 0.811 s
Find: Δy
Δy = v₀ t + ½ at²
Δy = (68 sin 25°) (0.811 s) + ½ (-9.8 m/s²) (0.811 s)²
Δy = 20.1 m