200 years has passed and now it is year 2220. The Earth is out of basic resources
as they have been drastically drained in the past 200 years. The president of the
United World Council (UWC) has approved you and your crew’s Mission to
Mars. You will pilot the most advanced spaceship the world has ever known, the
Excelsior! It will carry equipment that will help to transform Mars so as to
resemble the Earth, especially so that it can support human life.
Before the mission can launch a few items need to be figured out. What is the
capacity of the fuel tank? How long should the fuel burn to achieve escape
velocity (otherwise the Excelsior will be stuck in the Earth’s gravitational pull)?
How long will it take the Excelsior to arrive at Mars?
1. The ground crew is filling the fuel tanks. You know th
Transcribed Image Text:4. The trajectory of the spaceship Excelsior during the first 5 minutes of the launch can be represented by an equation for its altitude H(T): = 2008 – 0.047T3 + 18.3T2 – 345T - and an equation for its downrange distance due-east R(T) = 4680e0.029T where the distances are provided in units of feet. a) Use the parametric equations for h(T) and R(T) to determine the equation for the speed, S, of the Excelsior along its trajectory where 2 2 ds dH + %D dt dt b) Determine the formula for the magnitude of the acceleration of the spaceship Excelsior using the second time derivatives of the parametric equations.

Question

200 years has passed and now it is year 2220. The Earth is out of basic resources
as they have been drastically drained in the past 200 years. The president of the
United World Council (UWC) has approved you and your crew’s Mission to
Mars. You will pilot the most advanced spaceship the world has ever known, the
Excelsior! It will carry equipment that will help to transform Mars so as to
resemble the Earth, especially so that it can support human life.
Before the mission can launch a few items need to be figured out. What is the
capacity of the fuel tank? How long should the fuel burn to achieve escape
velocity (otherwise the Excelsior will be stuck in the Earth’s gravitational pull)?
How long will it take the Excelsior to arrive at Mars?
1. The ground crew is filling the fuel tanks. You know th

4. The trajectory of the spaceship Excelsior during the first 5 minutes of the
launch can be represented by an equation for its altitude
H(T):
= 2008 – 0.047T3 + 18.3T2 – 345T
-
and an equation for its downrange distance due-east
R(T) = 4680e0.029T
where the distances are provided in units of feet.
a) Use the parametric equations for h(T) and R(T) to determine the equation
for the speed, S, of the Excelsior along its trajectory where
2
2
ds
dH
+
%D
dt
dt
b) Determine the formula for the magnitude of the acceleration of the
spaceship Excelsior using the second time derivatives of the parametric
equations.

Accepted Answer

Velocity
The velocity of an object is defined by the rate of change of displacement. If the change…