Answer:
A) 199.78 J
B) 9.292x10^14 J
C) 4.2x10^7 m/s
D) 0.65 m
E) 1.13x10^-8 sec
D) 2.94x10^-9 sec
Explanation:
mass of ball = 0.0580 kg
A)
If smashed at v = 83.0 m/s, KE is
KE = 0.5mv^2
= 0.5 x 0.0580 x 83.0^2
= 199.78 J
B) if returned at v = 1.79×10^8 m/s, KE will be
KE = 0.5mv^2
= 0.5 x 0.0580 x (1.79×10^8)^2
= 9.292x10^14 J
C) during Einstein's return, velocity of rabbit relative to players is
Vr = 2.21×108 m/s
Rabbit's velocity relative to ball = 2.21×10^8 - 1.79×10^8
= 4.2x10^7 m/s
D) the rabbit's speed approaches the speed of light so we consider relativistic effect. The rabbit's measured distance is
l = l°( 1 - v^2/c^2)
= 2.5(1 - 2.21/3)
= 2.5 x 0.26
= 0.65 m
E) according to the players, the time taken by the rabbit is
t = d/v = 2.5/ 2.21×10^8
= 1.13x10^-8 sec
F) the time for rabbit as measured by rabbit is relativistic
t = t°( 1 - v^2/c^2)
= 1.13x10^-8 (1 - 2.21/3)
= 1.13x10^-8 x 0.26
= 2.94x10^-9 sec
I believe the correct
form of the energy function is:
u (x) = (3.00 N)
x + (1.00 N / m^2) x^3
or in simpler
terms without the units:
u (x) = 3 x +
x^3
Since the
highest degree is power of 3, therefore there are two roots or solutions of the
equation.
Since we are to
find for the positions x in which the force equal to zero, u (x) = 0,
therefore:
3 x + x^3 = u
(x)
3 x + x^3 = 0
Taking out x:
x (3 + x^2) = 0
So one of the
factors is x = 0.
Finding for the
other two factors, we divide the two sides by x and giving us:
x^2 + 3 = 0
x^2 = - 3
x = sqrt (- 3)
x = - 1.732 i, 1.732
i
The other two
roots are imaginary therefore the force is only equal to zero when the position
is also zero.
Answer:
x = 0
Answer:
0.6 m/s
Explanation:
2Hz = 2^-1 = 2 /s
30cm = .3m
Velocity is in the units m/s, so multiplying wavelength in meters by the frequency will give you the velocity.
(.3m)*(2 /s) = 0.6 m/s
62 liters or 62.640 if you need decimal.
