Space Shuttle Launch Problem
Okay, I've been trying to figure this out for a while now, and after trying seemingly everything, I'm still lost. Can anyone help? Thanks in advance!
- The trajectory of the Space Shuttle during the first 5 minutes of the launch of STS-30 can be represented by an equation for its altitude: h(T) = 2008 - 0.047 T3 + 18.3 T2 - 345T
and an equation for its down-range distance due East: R(T) = 4680 e0.029T
where the distances are provided in units of feet commonly used by NASA engineers for describing trajectories near earth. The problems below will use these 'parametric equations of motion' to determine the time of the highest acceleration.
Problem 1 - Use the parametric equations for h(T) and R(T) to determine the equation for the speed, S, of the Shuttle along its trajectory where dS/dt = ( (dh/dt)2 + (dR/dt)2 )1/2
Problem 2 - Determine the formula for the magnitude of the acceleration of the Shuttle using the second time derivatives of the parametric equations.
Problem 3 - From your answer to Problem 2,
- a) find the time at which the acceleration is an extremum, and specifically, a maximum along the modeled trajectory. (round to the first decimal place)
- b) What is the acceleration in feet/sec2 at this time (round to the nearest whole number)?
- c) If the acceleration of gravity at the earth's surface is 32 feet/sec2, how many 'Gs' did the astronauts pull at this time (round to the first decimal)?