A single stage rocket is fired from a launch pad just in front of the Library. T

Question

A single stage rocket is fired from a launch pad just in front of the Library. The rocket engines impart a constant acceleration of 20 m/sec/sec for a total time of 40 sec. At that time, there is no more fuel in the rocket engine and the rocket continues upwards in free fall (g=0 ft/sec/sec). (a) How high will the rocket reach before it begins to fall back to the campus? (b) How long did it take for the rocket to reach that maximum height? (c) You, the designer of the rocket, are now told that you must make adjustments so that the next rocket will reach a maximum height 1 km higher than the maximum height reached by the first rocket. What adjustments can you make - explain?

Explanation / Answer

Alright, first off, what IS the maximum height? The highest point of an upside down parabola is the vertex right? How do you find the vertex? -b/2a h(t) = -16t^2 + 100t + 1 a = -16 b = 100 c = 1 -100/2(-16) = 3.125 Now plug that in for t to find your h(t), which will be your max height. h(t) = -16(3.125)^2 + 100(3.125) + 1 = 157.25 Ok so your max height is 157.25 feet. Now you can solve for t (time it takes to get to 157.25 feet in the air). 157.25 = -16t^2 + 100t + 1 -157.25 -157.25 0 = -16t^2 + 100t - 156.25 Now use the quadratic formula to solve for t. Then that's your answer.

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