Answer:
the maximum possible constant speed is 8 m/sec
Explanation:
from the image, Given that
r(t) = (2t, t²,t²/3), -5 ≤ t ≤ 5
Given that the curvature K(t) = 2 / ( t² + 2)²
note that t² + 2 ≥ 2
(t² + 2)² ≥ 4
1 / (t² + 2)² ≤ 1/4
2 / (t² + 2)² ≤ 1/2
Also note that k(0) = 1/2
The normal component of acceleration satisfies aN = kv²
where v = ║v(t)║is the speed of the roller coaster.
The maximum possible normal component of acceleration is 32
so, aN ≤ 32 every where on the track
aN = kv² ≤ 1/2v² ≤ 32
v² ≤ 64
Therefore, the maximum possible constant speed is 8 m/sec
Answer:
4v/3
Explanation:
Assume elastic collision by the law of momentum conservation:
where v is the original speed of car 1, v1 is the final speed of car 1 and v2 is final speed of car 2. m1 and m2 are masses of car 1 and car 2, respectively
Substitute
Divide both side by , then multiply by 6 we have
So the final speed of the second car is 4/3 of the first car original speed
Answer:
The number of people at game are approximately 22909
Explanation:
Given data
When one person shout
When n number of person shout together
The sound intensity level during one person shout is given by:
The sound intensity level during n number of person shout is given by:
Since each person generates same sound intensity and hence total number of persons can be determined as
Hence
The number of people at game are approximately 22909