Answer:
speed of plane in still air = 1060 km/h
speed of wind = 170 km/h
Explanation:
Let teh speed of plane in still air is vp and the speed of air is va.
Irt travels 2670 km in 3 hours against the wind
So,
vp - va = 2670 / 3 = 890 km/h ..... (1)
It travels 11070 km in 9 hours along the wind.
vp + va = 11070 / 9 = 1230 km/h .... (2)
Adding both the equations
2 vp = 2120
vp = 1060 km/h
and va = 1230 - vp = 1230 - 1060 = 170 km/h
Answer:
Pressure,
Explanation:
It is given that,
Mass of the woman, m = 55 kg
Diameter of the circular cross section, d = 6 mm
Radius, r = 3 mm = 0.003 m
Let P is the pressure exerted on the floor. It is equal to the force acting on woman per unit area. It is given by :




So, the pressure exerted on the floor is
. Hence, this is the required solution.
When light moves from a medium with higher refractive index to a medium with lower refractive index, the critical angle is the angle above which there is no refracted light, and all the light is reflected. The value of this angle is given by

where n2 and n1 are the refractive indices of the second and first medium, respectively.
In the first part of the problem, light moves from glass to air (

) and the critical angle is

. This means that we can find the refractive index of glass by re-arranging the previous formula:

Now the glass is put into water, whose refractive index is

. If light moves from glass to water, the new critical angle will be
To solve the problem it is necessary to apply conservation of the moment and conservation of energy.
By conservation of the moment we know that

Where
M=Heavier mass
V = Velocity of heavier mass
m = lighter mass
v = velocity of lighter mass
That equation in function of the velocity of heavier mass is

Also we have that 
On the other hand we have from law of conservation of energy that

Where,
W_f = Work made by friction
KE = Kinetic Force
Applying this equation in heavier object.






Here we can apply the law of conservation of energy for light mass, then

Replacing the value of 

Deleting constants,


Answer:

Explanation:
Let assume that one end of the spring is attached to the ground. The speed of the metal block when hits the relaxed vertical spring is:


The maximum compression of the spring is calculated by using the Principle of Energy Conservation:

After some algebraic handling, a second-order polynomial is formed:


The roots of the polynomial are, respectively:


The first root is the only solution that is physically reasonable. Then, the elongation of the spring is:

The maximum height that the block reaches after rebound is:

