According to Kepler's harmonic law, Neptune would have a _________ orbit around the Sun than Mercury.
2 answers:
Slower
Explanation:
Kepler's harmonic law (also called Kepler's third law) states that:
"The cube of the radius of the orbit of a planet around the sun is proportional to the square of its period of revolution"
In formula, this can be written as
where
r is the radius of the orbit
T is the orbital period
const. is a constant number, which is the same for all the planets orbiting the sun
By looking at the equation, we can see that the further a planet from the sun, the larger its orbital period: this means that the further planet will have a slower orbit. In this problem, we have to compare Neptune and Mercury: since Neptune is further from the sun than Mercury, also its orbital period will be larger, and therefore Neptune would have a slower orbit around the Sun than Mercury.
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Hi there!
We can begin by calculating the time the ball takes to reach the highest point of its trajectory, which can be found using the following:
Where:
tmax = (? sec)
vsinθ = vertical comp. of velocity = 10sin(48) = 7.43 m/s)
g = acceleration due to gravity (9.8 m/s²)
We can solve for this time:
When the ball is at the TOP of its trajectory, its VERTICAL velocity is equivalent to 0 m/s. Thus, we can consider this a free-fall situation.
We must begin by solving for the maximum height reached by the ball using the equation:
d = displacement (m)
vi = initial velocity (7.43 m/s)
a = acceleration due to gravity
d = displacement (m)
y0 = initial VERTICAL displacement (28m)
Plug in the values:
Now, we can use the rearranged kinematic equation:
Add the two times together: