<u>Yes. The speed of a rocket can exceed the exhaust speed of the fuel.</u>
How this is explained?
- The thrust of the rocket does not depend on the relative speed of the gases or the relative speed of the rocket.
- It depends on conservation of momentum.
What is conservation of momentum?
- Conservation of momentum, general law of physics according to which the quantity called momentum that characterizes motion never changes in an isolated collection of objects; that is, the total momentum of a system remains constant.
- Momentum is equal to the mass of an object multiplied by its velocity and is equivalent to the force required to bring the object to a stop in a unit length of time.
- For any array of several objects, the total momentum is the sum of the individual momenta.
- There is a peculiarity, however, in that momentum is a vector, involving both the direction and the magnitude of motion, so that the momenta of objects going in opposite directions can cancel to yield an overall sum of zero.
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Answer:
Because it can easily resist air resistance.
Explanation:
Since air resistance is not negligible, the crumpled paper will reach the ground first because it can easily resist air resistance surrounding it compare to the un-crumpled one that will be influenced by the air thereby causing the un-crumpled paper to spend more time in the air
Answer:
The final velocity of the thrower is
and the final velocity of the catcher is
.
Explanation:
Given:
The mass of the thrower,
.
The mass of the catcher,
.
The mass of the ball,
.
Initial velocity of the thrower, 
Final velocity of the ball, 
Initial velocity of the catcher, 
Consider that the final velocity of the thrower is
. From the conservation of momentum,

Consider that the final velocity of the catcher is
. From the conservation of momentum,

Thus, the final velocity of thrower is
and that for the catcher is
.
Answer:
Explanation:
Let the angle between the first polariser and the second polariser axis is θ.
By using of law of Malus
(a)
Let the intensity of light coming out from the first polariser is I'
.... (1)
Now the angle between the transmission axis of the second and the third polariser is 90 - θ. Let the intensity of light coming out from the third polariser is I''.
By the law of Malus

So,



(b)
Now differentiate with respect to θ.


The amount of metal in a closed cylindrical can that is 10 cm high and 4 cm in diameter if the metal on the top and the bottom is 0.1 cm thick and the metal on the sides is 0.05 cm thick is 8.8 cm.
The formula for calculating the volume of a cylinder is given below.
V = πr^2 h
Get the differential of the volume as shown:
dV = V/ h dh + V / r dr
V/ h = πr^2
V/ h = 2 πr h
Now, the differential becomes
dV = πr^2dh + 2πrh dr
Given the following parameters i.e. diameter and height
dh = 0.1 + 0.1 = 0.2 cm
dr = 0.05 cm
h = 10 cm
d = 4 cm
r = 2cm
Substituting the values in the above equation, we get
dV = 3.14(2)^2(0.2) + 2(3.14)(2)(10)(0.05)
dV = 2.512 + 6.28
dV = 8.792 cm
dV = 8.8 cm
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