First I’ll show you this standard derivation using conservation of energy:
Pi=Kf,
mgh = 1/2 m v^2,
V = sqrt(2gh)
P is initial potential energy, K is final kinetic, m is mass of object, h is height from stopping point, v is final velocity.
In this case the height difference for the hill is 2-0.5=1.5 m. Thus the ball is moving at sqrt(2(10)(1.5))=
5.477 m/s.
Answer:
2.726472 s more or 1.5874 times more time is taken than 10-lb roast.
Explanation:
Given:
- The cooking time t is related the mass of food m by:
t = m^(2/3)
- Mass of roast 1 m_1 = 20 lb
- Mass of roast 2 m_2 = 10 lb
Find:
how much longer does a 20-lb roast take than a 10-lb roast?
Solution:
- Compute the times for individual roasts using the given relation:
t_1 = (20)^(2/3) = 7.36806 s
t_2 = (10)^(2/3) = 4.641588 s
- Now take a ration of t_1 to t_2, to see how many times more time is taken by massive roast:
t_1 / t_2 = (20 / 10)^(2/3)
- Compute: t_1 / t_2 = 2^(2/3) = 1.5874 s
- Hence, a 20-lb roast takes 1.5874 times more seconds than 10- lb roast.
t_2 - t_1 = 2.726472 s more
Look it up on google copy and paste
Answer:

Explanation:
Use the equation:
(where T is the period)
(9 comes from the period of a full wavelength)

Answer:
The spring's maximum compression will be 2.0 cm
Explanation:
There are two energies in this problem, kinetic energy
and elastic potential energy
(with m the mass, v the velocity, x the compression and k the spring constant. ) so the total mechanical energy at every moment is the sum of the two energies:

Here we have a situation where the total mechanical energy of the system is conserved because there are no dissipative forces (there's no friction), so:


Note that at the initial moment where the hockey puck has not compressed the spring all the energy of the system is kinetic energy, but for a momentary stop all the energy of the system is potential elastic energy, so we have:

(1)
Due conservation of energy the equality (1) has to be maintained, so if we let k and m constant x has to increase the same as v to maintain the equality. Therefore, if we increase velocity to 2v we have to increase compression to 2x to conserve the equality. This is 2(1.0) = 2.0 cm