Answer:
There are finally 4 rotations per second.
Explanation:
If a trapeze artist rotates once each second while sailing through the air, and contracts to reduce her rotational inertia to one fourth of what it was. We need to find the final angular velocity. It is a case of conservation of angular momentum such that :
Let ,
and
So,
So, there are finally 4 rotations per second. Hence, this is the required solution.
This question involves the concepts of the law of conservation of energy, kinetic energy, and potential energy.
The height of the hill is "166.76 m".
<h3>LAW OF CONSERVATION OF ENERGY:</h3>According to the law of conservation of energy at the highest point of the roller coaster ride, that is, the hill, the whole (maximum) kinetic energy of the roller coaster is converted into its potential energy:
where,
Therefore,
<u>h = 166.76 m</u>
Learn more about the law of conservation of energy here:
Answer:
(a) 62.5 m
(b) 7.14 s
Explanation:
initial speed, u = 35 m/s
g = 9.8 m/s^2
(a) Let the rocket raises upto height h and at maximum height the speed is zero.
Use third equation of motion
h = 62.5 m
Thus, the rocket goes upto a height of 62.5 m.
(b) Let the rocket takes time t to reach to maximum height.
By use of first equation of motion
v = u + at
0 = 35 - 9.8 t
t = 3.57 s
The total time spent by the rocket in air = 2 t = 2 x 3.57 = 7.14 second.
Answer:
Focal length, f = 16 cm
Explanation:
Image distance, v = 24 cm
Object distance, u = -48 cm
We need to find the focal length of the lens. It can be determined using the lens formula as :
f = 16 cm
So, the focal length of the converging lens is 16 cm. Hence, this is the required solution.