The change in kinetic energy of the car is equivalent to the change in its potential energy. Thus:
K.E = P.E
1/2 x mΔv² = mgΔh
h = (8.2² - 5²) / 2(9.81)
h = 2.15 meters
Answer:
Solution
Explanation:
Solution:-
- The direction of motion of bus and car can be denoted by velocity vectors ( v1 and v2 ) respectively.
- On a page draw the velocity vector v1 vertically up denoting the direction of motion of bus from origin
- Similarly,draw the velocity vector v1 horizontally left denoting the direction of motion of car from origin.
- The force exerted by the car-bus interaction is always in the direction of motion.
- The force exerted by the bus is parallel to velocity vector as F1 and force exerted by the car is parallel to velocity vector as F2.
- The vector addition of of the two forces ( F1 and F2 ) will tell us the direction and magnitude of resultant force due to car-bus interaction.
- The resultant force will cause the car to be pushed off the road in the direction shown in the diagram.
This is a Doppler effect. Generally, if you move to a frequency source, you would detect an increase in frequency and when you move away from a source you would detect a decrease.
For this question, before you pass them, you are actually approaching them, so you would hear a higher frequency than the constant 300 Hz they are playing at.
Using the condensed formula:
f ' = ((v <u>+</u> vd)/(v <u>+</u> vs)) * f
Where: vd = Velocity of the detector.
vs = Velocity of the frequency source.
v = Velocity of sound in air.
f ' = Apparent frequency.
f = Frequency of source.
v = 343 m/s, vd = detector = 27.8 m/s, vs = velocity of the source =0. (the flautists are not moving).
f = 300 Hz.
There would be an overall increase in frequency, so we maintain a plus at the numerator and a minus at the denominator.
f ' = ((v + vd)/(v - vs)) * f
f ' = ((343+ 27.8)/(343 - 0)) * 300
= (370.8/343)* 300 = 324.3
Therefore frequency before passing them = 324.3 Hz.
Cheers.
Answer:
The velocity is 
Explanation:
From the question we are told that
The mass of the ball is 
The radius is 
The force is 
The speed of the ball is 
Generally the kinetic energy at the top of the circle is mathematically represented as
=> 
=> 
Generally the work done by the force applied on the ball from the top to the bottom is mathematically represented as
Here d is the length of a semi - circular arc which is mathematically represented as
So
Generally the kinetic energy at the bottom is mathematically represented as
=> 
=> 
From the law of energy conservation
=> 
=>
