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
The acceleration is given as:
a = g sin(30°) where g is the gravitational acceleration
For g = 10 m/s^2, we get
a = 10 sin(30°) = 10 * 1/2 = 5 m/s^2
Hello there.
<span>It takes 3 minutes to make toast in a 1500 watt toaster. Calculate how much work is done by the toaster.
</span>270,000 J
Answer:
A sample of 5.2 mg decays to .65 mg or to 1/8 of its original amount.
1/8 = 1/2 * 1/2 * 1/2 or 3 half-lives.
3 * 30.07 = 90 yrs for 5.2 mg to decay to .65 mg
You can get these other numbers similarly:
5.2 / .0102 = 510 requires about 9 half-lives which is 30 * 9 = 270 yrs
Answer:
Wave W is a sound wave, Waves X and Y are light waves, and it is impossible to tell what kind of wave Wave Z is.
Explanation:
W travels fastest through metal
X travels fastest through air,
Y travels more slowly through water than air
Z travels more slowly at cool temperatures
W appears to be sound wave as sound travels fastest through metal .
X appears to be light wave as light travels fastest in air .
Y also appears to be light wave as speed of light is reduced when it passes from air to water .
Z It is impossible to tell anything about the nature of Z wave .
