Answer:
hmax = 1/2 · v²/g
Explanation:
Hi there!
Due to the conservation of energy and since there is no dissipative force (like friction) all the kinetic energy (KE) of the ball has to be converted into gravitational potential energy (PE) when the ball comes to stop.
KE = PE
Where KE is the initial kinetic energy and PE is the final potential energy.
The kinetic energy of the ball is calculated as follows:
KE = 1/2 · m · v²
Where:
m = mass of the ball
v = velocity.
The potential energy is calculated as follows:
PE = m · g · h
Where:
m = mass of the ball.
g = acceleration due to gravity (known value: 9.81 m/s²).
h = height.
At the maximum height, the potential energy is equal to the initial kinetic energy because the energy is conserved, i.e, all the kinetic energy was converted into potential energy (there was no energy dissipation as heat because there was no friction). Then:
PE = KE
m · g · hmax = 1/2 · m · v²
Solving for hmax:
hmax = 1/2 · v² / g
Answer:
Option D 3.9
Explanation:
First, you need to use the correct equation which is the following:
COP = Q/W
Where:
Q = heat absorbed
W = work done by the pump
COP = coefficient of perfomance
We have all the data, so, all you need to do is replace in the above expression and you shoould get the correct result:
COP = 30 / 7.7
COP = 3.896
This result you can round it to 3.9. option D.
I couldnt type it out so here's a picture
The magnetic force (Lorentz force) experienced by the proton in the magnetic field is given by

since

, because the velocity v and the force F in this problem are perpendicular, and so also the angle

between the velocity and the magnetic field B should be

.
Let's find the magnitude of the magnetic field; this is given by

To understand the direction, let's use the right-hand rule:
-index finger: velocity
- middle finger: magnetic field
- thumb: force
Since the velocity (index) points east and the force (thumb) points south, then the magnetic field (middle finger) points downwards. So we write:
B = -0.091 T
Diffraction means spreading out of waves that has the same wavelength as the size of the gap. Sound waves have high wavelength and so it diffracts\spreads out and enables anyone to hear your voice from anywhere outside the room.
For inside the room, the sound waves doesn't actually diffract. They collide with the air particles, causing a series of compressions and rarefactions which spreads out in the air particles and anyone can hear your voice.
Air is the medium for the sound waves to travel.