Answer:
a. There is a force on Jupiter toward the center of the orbit.
d. Jupiter is accelerating toward the center of the orbit.
Explanation:
Let us look at each of the choices one by one:
a. There is a force on Jupiter toward the center of the orbit.
True. The sun being at the center of Jupiter's orbit, pulls the planet towards it (providing the centripetal force), therefore, there exists a force on Jupiter toward the center of the orbit.
b. There is a force on Jupiter pulling it out from the center of the orbit.
Nope. The centripetal force due to gravity acts towards the center of the orbit.
c. There is a force on Jupiter in the direction of its motion.
Nope. There exists only the centripetal force acting towards the center of the orbit,
d. Jupiter is accelerating toward the center of the orbit.
Yes. Because of the centripetal force gravity provides, Jupiter is accelerating towards the center of the orbit, but it does not fall in because it has velocity perpendicular to the direction of its acceleration.
One thing thats the same is there both universes.
One thing diffrent is that in the milky way there is proven life on earth but ursa major is proven without life.
Kinetic energy is equal to half of an objects mass multiplied by the velocity squared.
Consider the projectile launched at initial velocity V at angle θ relative to the horizontal.
Neglect wind or aerodynamic resistance.
The initial vertical velocity is Vsinθ.
When the projectile reaches its maximum height of h, its vertical velocity will be zero.
If the time taken to attain maximum height is t, then
0 = Vsinθ - gt
t = (Vsinθ)/g, where g = acceleration due to gravity.
The horizontal component of launch velocity is Vcosθ. This velocity remains constant because aerodynamic resistance is ignored.
The time to travel the horizontal distance D is twice the value of t.
Therefore
D = Vcosθ*[(2Vsinθ)/g]
= (2V²sinθ cosθ)/g
= (V²sin2θ)/g
In order for D (horizontal distance) to be maximum,

That is,

Because

, therefore cos(2θ) = 0.
This is true when 2θ = π/2 => θ = π/4.
It has been shown that the maximum horizontal traveled can be attained when the launch angle is π/4 radians, or 45°.