Answer:
Because of the speed of the sound.
Explanation:
The first thing that happens in such cases is to take into account the speed of the sound. First, we see that the player hits the ball with the bat, if we are in the stands far enough we will hear the sound of the batting time later, this time depends on the speed of the sound which is equal to 345 [m/s].
Another visible and practical example is a fireworks display, where people nearby immediately hear the explosion. while those at a great distance will be able to see first the explosion followed by the sound.
With the following equation, we can calculate how long it takes to hear a hit or explosion
t = x / v
where:
x = distance [m]
v = sound velocity = 345 [m/s]
t = time [s]
Answer:
22 degree
Explanation:
Angle of incidence, i = 30 degree
the refractive index of water with respect to air is 4/3.
As the ray of light travels from rarer medium to denser medium, that mean air to water, the refraction takes place.
According to Snell's law,
Refractive index of water with respect to air = Sin i / Sin r
Where, r be the angle of refraction
4 / 3 = Sin 30 / Sin r
0.75 = 2 Sin r
Sin r = 0.375
r = 22 degree
Thus, the angle of refraction is 22 degree.
Answer:
The maximum mass that can fall on the mattress without exceeding the maximum compression distance is 16.6 kg
Explanation:
Hi there!
Due to conservation of energy, the potential energy (PE) of the mass at a height of 3.32 m will be transformed into elastic potential energy (EPE) when it falls on the mattress:
PE = EPE
m · g · h = 1/2 k · x²
Where:
m = mass.
g = acceleration due to gravity.
h = height.
k = spring constant.
x = compression distance
The maximum compression distance is 0.1289 m, then, the maximum elastic potential energy will be the following:
EPE =1/2 k · x²
EPE = 1/2 · 65144 N/m · (0.1289 m)² = 541.2 J
Then, using the equation of gravitational potential energy:
PE = m · g · h = 541.2 J
m = 541.2 J/ g · h
m = 541.2 kg · m²/s² / (9.8 m/s² · 3.32 m)
m = 16.6 kg
The maximum mass that can fall on the mattress without exceeding the maximum compression distance is 16.6 kg.
Answer:
(a) r = 1.062·R
= 
(b) r = 
(c) Zero
Explanation:
Here we have escape velocity v
given by
and the maximum height given by
Therefore, when the initial speed is 0.241v we have
v = 
so that;
v² = 
v² = 
is then
Which gives
or
r = 1.062·R
(b) Here we have
Therefore we put 
in the maximum height equation to get
From which we get
r = 1.32·R
(c) The we have the least initial mechanical energy, ME given by
ME = KE - PE
Where the KE = PE required to leave the earth we have
ME = KE - KE = 0
The least initial mechanical energy to leave the earth is zero.
