Question

Assuming an object has a total mass of M and gravitational constant on earth = g, air resistance = Cd, total surface area = A, initial height = H, and this object has a thruster (assuming constant thrust = F_thrust) that ignites at a time T_ignition and stops burning at time T_turnoff (T_turnoff and T_ignition occur at different time during the process), please derive an equation for the velocity of this linear vertical motion as a function of time, V(t).

Answer #1

In this problem, you are going to explore three different ways
to determine the gravitational constant G.
Part (a) By observing that the centripetal
acceleration of the Moon around the Earth is ac
= 2.65 × 10-3 m/s2, what is the gravitatonal
constant G, in cubic meters per kilogram per square
second? Assume the Earth has a mass of ME =
6.02 × 1024 kg, and the mean distance between the
centers of the Earth and Moon is rm =...

A 2400-kg test rocket is launched vertically from the launch
pad. Its fuel (of negligible mass) provides a thrust force so that
its vertical velocity as a function of time is given by
v(t)=At+Bt2, where A and B are constants and time is measured from
the instant the fuel is ignited. At the instant of ignition, the
rocket has an upward acceleration of 1.90 m/s2 and 1.20 s later an
upward velocity of 1.50 m/s .
Part A) Determine A....

Which one of the following statements is not possible?
An object has zero velocity and non-zero acceleration
An object travels with a northward velocity and a northward
acceleration
An object travels with a constant velocity and a constant
non-zero acceleration
An object travels with a changing velocity and a constant
acceleration
____________
In a displacement vs. time graph, a sloped (non-horizontal)
line indicates:
The object is moving with constant, non-zero, acceleration
The total displacement of the object is zero...

A balloon filled with gaș has a radius R and mass M. The gas was
extracted from the Moon and will be launched into Earth by a
rocket. Before taking off, the center of the balloon is at a height
d. The rocket ignites and gives the balloon F. a constant push up.
While the rocket is on, it sinks the surface of the glube a
distance r.
1. Calculate the kinetic energy of the balloon when it is at...

Two objects are dropped from the same height on earth. One has a
mass three times greater than the other one. If they are dropped at
the same time, assuming no air resistance, which of the following
statements is true?
The acceleration is the same for both objects, but the force on the
lighter object is greater.
The lighter object experiences one-third the force of the heavier
object, but the acceleration of the two objects are the same.
The lighter...

Consider a satellite of mass m in a circular orbit of radius r
around the Earth of mass ME and radius RE.
1.
What is the gravitational force (magnitude and direction) on
the satellite from Earth?
2.
If we define g(r) to be the force of gravity on a mass m at a
radial distance r from the center of the Earth, divided by the mass
m, then evaluate the ratio g(r)/g(RE)to see how g varies with
radial distance. If...

A 50.0-g object connected to a spring with a force constant of
100.0 N/m oscillates on a horizontal frictionless surface with an
amplitude of 8.00 cm.
a) What is the period (in seconds) and frequency of its
motion?
b) Assuming that the object's equilibrium position (i.e. when
the spring is unstretched) is designated as x = 0, and that at t =
0 the object is located at maximum amplitude, x(t) = A cos (ωt),
describes the motion. What is...

1. A body is launched upward at 30 m/s. After how much time is
the object moving with half the initial speed, but in the downward
direction to the nearest hundredth of a second?
2. A girl launches a ball straight up into the air on Earth. The
average velocity of the ball from launch point until it attains its
maximum height is 24 m/s. Ignore air resistance.
What is the maximum height above the launch point to the nearest...

An object of mass m = 0.25 kg has a horizontal spring attached
to its left side, and slides along a frictionless surface. The
spring constant is κ = 0.4 N m . At t = 0 s, the object is
displaced 0.1m to the right of its equilibrium position. Its
initial velocity is 0.4 m s , toward the right.
a) Calculate the period T of the motion. b) Calculate the
angular frequency ω. c) Calculate the frequency ν....

Speed means the absolute value of the velocity, hence it is
always non-negative. While the sign of the velocity indicates the
direction of the motion, the speed is insensitive to the direction.
For example, speed is the value displayed by car’s speedometer; it
does not indicate the direction of driving (e.g., northbound versus
southbound). At time t = 0 seconds (s) an object has zero velocity
and it starts a free fall from the altitude of 1200 metres (m)
above...

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