Answer:
Work done = 35467.278 J
Explanation:
Given:
Height of the cone = 4m
radius (r) of the cone = 1.2m
Density of the cone = 600kg/m³
Acceleration due to gravity, g = 9.8 m/s²
Now,
The total mass of the cone (m) = Density of the cone × volume of the cone
Volume of the cone = 
thus,
volume of the cone = 
= 6.03 m³
therefore, the mass of the cone = 600 Kg/m³ × 6.03 m³ = 3619.11 kg
The center of mass for the cone lies at the 
times the total height
thus,
center of mass lies at, h' = 
Now, the work gone (W) against gravity is given as:
W = mgh'
W = 3619.11kg × 9.8 m/s² × 1 = 35467.278 J
It doesn't matter. If the slides are truly frictionless, then
your kinetic energy at the bottom will be equal to the
potential energy you had at the top, no matter what kind
of route you took getting down.
___________________________
The only way I can think of that it would make a difference
would be if the shallow slide were REALLY REALLY long,
and you didn't have anything to eat all the way down.
Then you might lose some weight while you're on the slide,
and your mass might be less at the bottom than it was at the
top. Then, in order to have the same kinetic energy at the
bottom, you'd need to be going a little bit faster.
But if it takes less than, say, two or three days, to go down the
long, shallow slide, then this effect would probably be too small
to make any difference.
Answer:
R=3818Km
Explanation:
Take a look at the picture. Point A is when you start the stopwatch. Then you stand, the planet rotates an angle α and you are standing at point B.
Since you travel 2π radians in 24H, the angle can be calculated as:
t being expressed in hours.
From the triangle formed by A,B and the center of the planet, we know that:
Solving for r, we get:
Since, A is a vector. Hence, we can break it into two components (x and y)
Angle made by the velocity vector A with the x-axis = 51.7°
Magnitude of the vector A = 70 m/s
°
m/s
°
m/s
Hence, the option C is correct.
