These are the Kepler's laws of planetary motion.
This law relates a planet's orbital period and its average distance to the Sun. - Third law of Kepler.
The orbits of planets are ellipses with the Sun at one focus. - First law of Kepler.
The speed of a planet varies, such that a planet sweeps out an equal area in equal time frames. - Second law of Kepler.
Answer:
Maximum height reached by the ball is 32 meters.
Explanation:
It is given that,
If a baseball is project upwards from the ground level with an initial velocity of 32 feet per second, then it's height is a function of time. The equation is given as :
...........(1)
t is the time taken
s is the height attained as a function of time.
Maximum height achieved can be calculated as :


-16 t + 32 = 0
t = 2 seconds
Put the value of t in equation (1) as :

s = 32 meters
So, the maximum height reached by the ball is 32 meters. Hence, this is the required solution.
Answer:
a. k = (1/k₁ + 1/k₂)⁻¹ b. k = (1/k₁ + 1/k₂ + 1/k₃)⁻¹
Explanation:
Since only one force F acts, the force on spring with spring constant k₁ is F = k₁x₁ where x₁ is its extension
the force on spring with spring constant k₂ is F = k₂x₂ where x₁ is its extension
Let F = kx be the force on the equivalent spring with spring constant k and extension x.
The total extension , x = x₁ + x₂
x = F/k = F/k₁ + F/k₂
1/k = 1/k₁ + 1/k₂
k = (1/k₁ + 1/k₂)⁻¹
B
The force on spring with spring constant k₃ is F = k₃x₃ where x₃ is its extension
Let F = kx be the force on the equivalent spring with spring constant k and extension x.
The total extension , x = x₁ + x₂ + x₃
x = F/k = F/k₁ + F/k₂ + F/k₃
1/k = 1/k₁ + 1/k₂ + 1/k₃
k = (1/k₁ + 1/k₂ + 1/k₃)⁻¹
The process of determining the value of the individual forces acting upon an object involve an application of Newton's second law (Fnet<span>=m. a) and an application of the meaning of the </span>net force<span>.</span>