Answer:
204 m
Explanation:
When the marble is dropped from a certain height, its gravitational potential energy converts into kinetic energy. So the kinetic energy gained is equal to the variation of gravitational potential energy:

where
m is the mass of the marble
g = 9.8 m/s^2 is the acceleration of gravity
is the change in height
In this problem, we have
m = 50 g = 0.05 kg

Solving the formula for
, we find the necessary height from which the marble should be dropped:

Answer:
0.8m/s
Explanation:
Weight of mas,F=763 N
Mass of man=
By using 
Weight of flatcar=F'=3513 N
Mass of flatcar=
Total mass of the system=Mass of man+mass of flatcar=77.86+358.5=436.36 kg
Velocity of system=19.8m/s
Let v be the velocity of flatcar with respect to ground
Velocity of man relative to the flatcar=
Final velocity of man with respect to ground=v-4.68
By using law of conservation of momentum
Initial momentum=Momentum of car+momentum of flatcar






Initial speed of flatcar=Speed of system
Increase in speed=Final speed-initial speed=20.6-19.8=0.8m/s
The sketch of the system is: two strings, 1 and 2, are attached to the ceiling and to a third string, 3.The third string holds the bag of cement.
The free body diagram of the weight with the string 3, drives to the tension T3 = weihgt => T3 = 325 N
The other free body diagram is around the joint of the three strings.
In this case, you can do the horizontal forces equilibrium equation as:
T1* cos(60) - T2*cos(40) = 0
And the vertical forces equilibrium equation:
Ti sin(60) + T2 sin(40) = T3 = 325 N
Then you have two equations with two unknown variables, T1 and T2
0.5 T1 - 0.766 T2 = 0
0.866 T1 + 0.643T2 = 325
When you solve it you get, T1 = 252.8 N and T2 = 165 N
Answer: T1 = 252.8 N, T2 = 165N, and T3 = 325N
Answer:
The observer detects light of wavelength is 115 nm.
(b) is correct option
Explanation:
Given that,
Wavelength of source = 500 nm
Velocity = 0.90 c
We need to calculate the wavelength of observer
Using Doppler effect

Where, 


Hence, The observer detects light of wavelength is 115 nm.
The energy conservation and trigonometry we can find the results for the questions about the movement of the acrobat are;
a) The maximum speed is v = 4.89 m / s
b) The maximum height is h = 1.22 m
The energy conservation is one of the most fundamental principles of physics, stable that if there are no friction forces the mechanistic energy remains constant. Mechanical energy is the sum of the kinetic energy plus the potential energies.
Em = K + U
Let's write the energy in two points.
Starting point. Highest part of the oscillation
Em₀ = U = m g h
Final point. Lower part of the movement
= K = ½ m v²
Energy is conserved.
Emo =
m g h = ½ m v²
v² = 2 gh
Let's use trigonometry to find the height, see attached.
h = L - L cos θ
h = L (1- cos θ)
They indicate that the initial angle is tea = 48º and the length is L = 3.7 m, let's calculate.
h = 3.7 (1- cos 48)
h = 1.22 m
this is the maximum height of the movement.
Let's calculate the velocity.
v = 4.89 m / s
In conclusion using the conservation of energy and trigonometry we can find the results for the questions about the movement of the acrobat are;
a) The maximum speed is v = 4.89 m / s
b) The maximum height is h = 1.22 m
Learn more here: brainly.com/question/13010190