Answer:
Cosmic ray's frame of reference: 99,875 years
Stationary frame of reference: 501,891 years
Explanation:
First of all, we convert the distance from parsec into metres:

The speed of the cosmic ray is

where
is the speed of light. Substituting,

And so, the time taken to complete the journey in the cosmic's ray frame of reference (called proper time) is:

Converting into years,

Instead, the time elapsed in the stationary frame of reference is given by Lorentz transformation:

And substituting v = 0.98c, we find:

Answer:
The centripetal acceleration of the runner is
.
Explanation:
Given that,
A runner completes the 200 m dash in 24.0 s and runs at constant speed throughout the race. We need to find the centripetal acceleration as he runs the curved portion of the track. We know that the centripetal acceleration is given by :

v is the velocity of runner

Centripetal acceleration,

So, the centripetal acceleration of the runner is
. Hence, this is the required solution.
Answer:
- a.

- b.

Explanation:
<h3>
a.</h3>
The equation for the voltage V of discharging capacitor in an RC circuit at time t is:

where
is the initial voltage, and
is the time constant.
For our problem, we know

and

So





This gives us

and this is the time constant.
<h3>
b.</h3>
At t = 18.8 s we got:



Answer:
It's only 1.11 m/s2 weaker at 400 km above surface of Earth
Explanation:
Let Earth radius be 6371 km, or 6371000 m. At 400km above the Earth surface would be 6371 + 400 = 6771 km, or 6771000 m
We can use Newton's gravitational law to calculate difference in gravitational acceleration between point A (Earth surface) and point B (400km above Earth surface):

where G is the gravitational constant, M is the mass of Earth and r is the distance form the center of Earth to the object





So the gravitational acceleration at 400km above surface is only 0.885 the gravitational energy at the surface, or 0.885*9.81 = 8.7 m/s2, a difference of (9.81 - 8.7) = 1.11 m/s2.