Answer:
r1 = 5*10^10 m , r2 = 6*10^12 m
v1 = 9*10^4 m/s
From conservation of energy
K1 +U1 = K2 +U2
0.5mv1^2 - GMm/r1 = 0.5mv2^2 - GMm/r2
0.5v1^2 - GM/r1 = 0.5v2^2 - GM/r2
M is mass of sun = 1.98*10^30 kg
G = 6.67*10^-11 N.m^2/kg^2
0.5*(9*10^4)^2 - (6.67*10^-11*1.98*10^30/(5*10^10)) = 0.5v2^2 - (6.67*10^-11*1.98*10^30/(6*10^12))
v2 = 5.35*10^4 m/s
Answer: D(t) = 
Explanation: A harmonic motion of a spring can be modeled by a sinusoidal function, which, in general, is of the form:
y =
or y = 
where:
|a| is initil displacement
is period
For a Damped Harmonic Motion, i.e., when the spring doesn't bounce up and down forever, equations for displacement is:
or 
For this question in particular, initial displacement is maximum at 8cm, so it is used the cosine function:
period =
12 =
ω = 
Replacing values:

The equation of displacement, D(t), of a spring with damping factor is
.
Answer:

Explanation:
Since the universal SI unit for velocity is meters/second, let's convert ft/s to m/s:

We can use the following kinematics equation to solve this question:

What we know:
- The initial velocity,
, is
- (physics concept) The final velocity must be equal in magnitude but opposite in direction to the initial velocity (
) - Acceleration,
, is acceleration due to gravity at about
Solving for
:

Answer:25.61 m/s
Explanation:
Given
truck is moving eastbound with a velocity of 16 m/s
Velocity of truck 
SUV is moving south with a velocity of 20 m/s
Velocity of SUV in vector form 
Velocity of truck relative to the SUV


Magnitude of relative velocity is
