An experimental fireworks shell is launched vertically from point A with an init

Question

An experimental fireworks shell is launched vertically from point A with an initial velocity of magnitude v0 = 140 ft/sec. In addition to the acceleration due to gravity, an internal thrusting mechanism causes a constant acceleration component of 2.1g in the direction shown for the first 1.7 seconds of flight, after which the thruster ceases to function. Determine the maximum height h achieved, the total flight time t, the net horizontal displacement x from point A, and plot the entire trajectory. Neglect any acceleration due to aerodynamics.

Explanation / Answer

For 1.7 s ; y = v0*1.7 + 0.5*2.1*32.174*sin 51 *1.7^2 = 313.87 ft vy = 140 + 32.174*1.7 = 194.6958 ft/s vx = 2.1*32.174* cos 51 *1.7 = 72.28 ft/s x =0.5*2.1*32.174*cos 51*1.7^2 = 61.44 ft after 1.7 s; v =194.6958 -32.174*t = 0 t =6.05 s total time =2*6.05 +1.7 = 13.8 s h = 194.6958*6.05 -0.5*32.174*6.05^2 = 589.085 ft maximum height = 589.085 + 313.87 = 902.955 ft horizontal displacement = 72.28 ft/s* 12. 1 + 61.44 ft = 936.028 ft

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