EX5.2 Rocket Tracking

# EX5.2 Rocket Tracking - and time Knowing that the radar...

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Lesson 5 EX5.2 Rocket Tracking Apollo 16 Launch

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What Coordinate Systems should you use. We can calculate a radial distance and we are given a changing angle θ . We should choose polar. m r r r 1 . 5865 47 cos 4000 4000 cos 1 1 = ° = = θ Determine values of r at the two times s m r r r r t r r / 6 . 225 5 . 0 1 2 = - = = Determine approximate values of the time derivatives of r and theta and average radial distance. Substitute into velocity equation and find magnitude EX5.2 Rocket Tracking Solution: Problem Type: Find: Given: b=4km, θ 1 =47º, θ 2 =48º, t 2 -t 1 =0.5 sec Approximate speed of the Rocket Kinematics (Want motion without interest in forces involved) NASA plans to replace the space shuttle with a multi-stage similar to the old Apollo rockets. In order to track the rocket, NASA plans to use a tracking radar as shown in the figure. Instrumentation on the radar will be able to measure the angle,θ
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Unformatted text preview: and time. Knowing that the radar station is b=4 km from the launch pad at point B, determine approximately the speed of the rocket if θ =47º at a point in time and θ =48º 0.5 seconds later. Write out the expression for velocity in Polar Coordinates e r e r v r + = m r r 9 . 5977 48 cos 4000 2 2 = ° = s rad s / 0349 . / 2 5 . 1 2 = ° =-= m r r r r ave ave 5 . 5921 2 2 1 = + = s m v v e e v r / 306 7 . 206 6 . 225 0349 . 5 . 5921 6 . 225 2 2 = + = × + = Reflection: The speed is equal to 684 mph when the rocket is at an altitude of 14,575 ft. Since airplanes travel around 450 mph at cruising altitude, this number seems reasonable although possibly on the low side for a rocket?...
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EX5.2 Rocket Tracking - and time Knowing that the radar...

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