The potential energy of the block is given by:
V = m*g*h
m mass
g = 9.81m/s²
h height
The potential energy of a spring is given by:
V = 0.5 * k * x²
k spring constant
x compression of the spring
If the block starts from rest it has potential energy, but no kinetic energy. As it slides down the incline potential energy is converted into kinetic energy. When the block hits the spring the kinetic energy is converted into spring's potential energy. If the spring is fully compressed and the block is at rest again, the block has transferred all its energy into the spring. No energy is lost. So we can write:
m * g * h = 0.5 * k * x²
m = 0.5 kg
g = 9.81 m/s²
h = 2.5m * sin 37° = 1,5 m
x = 0,6 m
Solve for k.
k = 2 * m * g * h / x² = 40.8 N/m
Here's the formula for the distance covered by an accelerating body in some amount of time ' T '. This formula is incredibly simple but incredibly useful. It pops up so often in Physics that you really should memorize it:
D = 1/2 a T²
Distance = (1/2)·(acceleration)·(time²)
This question gives us the acceleration and the distance, and we want to find the time.
(9,000 m) = (1/2) (20 m/s²) (time²)
(9,000 m) = (10 m/s²) (time²)
Divide each side by 10 m/s²:
(9,000 m) / (10 m/s²) = (time²)
900 s² = time²
Square root each side:
<em>T = 30 seconds</em>
Answer:
The value is
Explanation:
From the we are told that
The initial speed of the object is
The greatest height it reached is 
Generally from kinematic equation we have that

At maximum height v = 0 m/s
So

=> 
Here H is the height from the initial height to the maximum height
So the initial height is mathematically represented as

=> 
=> 
Generally the time taken for the object to reach maximum height is mathematically evaluated using kinematic equation as follows

At maximum height v = 0 m/s

=> 
Generally the time taken for the object to move from the maximum height to the ground is mathematically using kinematic equation as follows

Here the initial velocity is 0 m/s given that its the velocity at maximum height
Also g is positive because we are moving in the direction of gravity
So

=> 
Generally the total time taken is mathematically represented as

=> 
=>
B) a rock being tossed high into the air
Answer:
Option A applies.
A. Greater than its escape speed from the mass within the volume
Explanation:
Here it is mentioned that the spherical volume is large enough for the space to be considered as homogeneous. Also, the pressure within the volume is negligible, so that will not result into the re collapse of the Universe. Now as per our knowing, Hubble's Law relates the average speed of the particle to the distance R between the Earth and the particle. So, if the particle's speed is greater than it's escape speed from the mass within the volume, then the Universe is bound to re collapse back again. Option A applies.