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 - 0.047 T^3 + 18.3 T^2 – 345T and an equation for its downrange distance due-east R(T) = 4680 e^0.029T 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 dS/dt= ( (dH/dt)^2 + (dR/dt)^2)^1/2 b) Determine the formula for the magnitude of the acceleration of the spaceship Excelsior using the second time derivatives of the parametric equations.
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 - 0.047 T^3 + 18.3 T^2 – 345T and an equation for its downrange distance due-east R(T) = 4680 e^0.029T 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 dS/dt= ( (dH/dt)^2 + (dR/dt)^2)^1/2 b) Determine the formula for the magnitude of the acceleration of the spaceship Excelsior using the second time derivatives of the parametric equations.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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 - 0.047 T^3 + 18.3 T^2 – 345T
and an equation for its downrange distance due-east
R(T) = 4680 e^0.029T
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
dS/dt= ( (dH/dt)^2 + (dR/dt)^2)^1/2
b) Determine the formula for the magnitude of the acceleration of the
spaceship Excelsior using the second time derivatives of the parametric
equations.
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