Answer:
80.386 degrees
Explanation:
We use the cosine equation here (which is the adjacent side of the unknown angle divided by the hypotenuse
The adjacent side = 699ft
The hypotenuse = 1034ft
using cos∅ = Adjacent/hypotenuse
where ∅ is the unknown angle
cos ∅ = 699/1034 = 0.167
∅ = arccos 0.167 = 80.368°
As easy as one can imagine
Explanation:
because the acceleration is negative, this indicates a deceleration (or slowing down) . Hence we can say that:
The car is decelerating (slowing down), i.e its velocity is decreasing, at a constant rate of 5m/s².
Answer:
Explanation:
Hi!
In order to obtain the Lagrangian of the system we must first write the Kinetic and Potential Energies. Lets orient our axes such that the axis of the cone coincide with the z axis. In cilindrical coordinates we have
- (1)
But, since the particle is constrained to move on the surface of the cilinder, we have the following relation between r and z:

or:
- (2)
and:
replacing (2) in (1) we obtain:
- (3)
Now the kinetic energy is given as:
- (4)
And the potential energy is given by:

So the Langrangian is given by:

And the equations of motion are:
For θ

For r

Obtained from the Euler-Langrange equations
Here the conserved quantity is given by the first equation of motion, namely:

Which is the magnitude of the angular momentum