The equation for potential energy is denoted as;
Pe = mgh,
where m = the mass, g = acceleration due to gravity, and h = vertical height of the apple. We are given the units for everything but height, which is also what we are solving for. We can then algebraically rearrange our initial equation to solve for h;
h = (Pe)/(mg)
Plug in your given units, and solve!
Post-check:
h = Pe/mg
h = 175J/(0.36g)(-9.81m/s^2)
h = appr. 49.5 meters
Note: Potential energy is a vector quantity; the displacement of the apple will be a negative number, but the distance itself, a scalar quantity, will be the absolute value of that.
Answers:
a) 5400000 J
b) 45.92 m
Explanation:
a) The kinetic energy 
of an object is given by:
Where:
is the mass of the train
is the speed of the train
Solving the equation:
This is the train's kinetic energy at its top speed
b) Now, according to the Conservation of Energy Law, the total initial energy is equal to the total final energy:
Where:
is the train's initial kinetic energy
is the train's initial potential energy
is the train's final kinetic energy
is the train's final potential energy, where 
is the acceleration due gravity and 
is the height.
Rewriting the equation with the given values:
Finding :
Answer:
1,920 Joules
Explanation:
K.E. = 1/2 mv2
so K.E. = 1/2 (60)(8x8) = 1,920 Joules
Answer:
B. has a smaller frequency
C. travels at the same speed
Explanation:
The wording of the question is a bit confusing, it should be short/long for wavelength and low/high for frequency. I assume low wavelength mean short wavelength.
All sound wave travel with the same velocity(343m/s) so wavelength doesn't influence its speed at all. It won't be faster or slower, it will have the same speed.
Velocity is a product of wavelength and frequency. So, a long-wavelength sound wave should have a lower frequency.
The option should be:
A. travels slower -->false
B. has a smaller frequency -->true
C. travels at the same speed --->true
D. has a higher frequency --->false
E. travels faster has the same frequency --->false
