Explanation:
The force of the roller-coaster track on the cart at the bottom is given by :
, m is mass of roller coaster
Case 1.
R = 60 m v = 16 m/s

Case 2.
R = 15 m v = 8 m/s

Case 3.
R = 30 m v = 4 m/s

Case 4.
R = 45 m v = 4 m/s

Case 5.
R = 30 m v = 16 m/s

Case 6.
R = 15 m v =12 m/s

Ranking from largest to smallest is given by :
F>E>A=B>C>D
Answer:
Self inductance, 
Explanation:
It is given that,
Length of the coil, l = 5 cm = 0.05 m
Area of cross section of the coil, 
Number of turns in the coil, N = 130
The self inductance relates the magnetic flux linkage to the current through the coil and it is given by :


L = 0.000127 Henry
or

So, the self inductance of the coil is 127 microhenry. Hence, this is the required solution.
Answer:
v = 2 cm/s
Explanation:
The equation of the wave is
y(x,t) = (2.0cm)*cos(2π*x−4π*t)
Where,
x is measured in cm
t in s
A more general formula for this equation would be
y(x,t) = A*cos(k*x−ω*t)
Where,
A = amplitude.
k = the wavenumber
ω = the angular frequency
The velocity of the wave corresponds to
v = ω/k
v = 4π / 2π = 2 cm/s
v = 2 cm/s
Answer:
Explanation:
mass of the astronaut including the spacesuit, 
distance of astronaut from the spaceship, d = 13 m
mass of the oxygen tank, m = 3 kg
Speed of tank with respect to spaceship, 
a)
<u>Using the conservation of linear momentum:</u>
total momentum before collision = total momentum after collision



b)
She mush hold her breath until she reaches the spaceship, i.e.


