Question

A model rocket is launched straight upward with an initial speed of 54.7 m/s. It accelerates with a constant upward acceleration of 1.94 m/s2 until its engines stop at an altitude of 131 m.

What is the maximum height reached by the rocket? How long after lift off does the rocket reach its maximum height?

How long is the rocket in the air?

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The picture below is the wrong calculations and answers. Please help!

Answer 1

By equation of kinematics u_2^2 = u_1^2 + 2a_1 h_1 = (54.7)^2 + 2 times 1.94 times 131 u_2 = 59.2 m/s h_2 is given by h_2 = u_2^2/2g = (59.2)^2/2 times 9.8 = 178.6 m Thus total height, H = h_1 + h_2 = (131 + 17836)m H = 309.6 m Maximum height reached Time taken h reach h_1 is t_1 (say) u_2 = u_1 + at_1 implies t_1 = 59.2 - 54.7/1.94 s = 2.32$ And to reach H_max from h_1, t_2 (say) t_2 = 59.2/9.8 $ = 6.04$ therefore Total time of left off, T = t_1 + t_2 = (2.32 + 6.04)s therefore T = 8.36$ left off time Time for which rocket is in air is t_4 = t_3 + T Now, t_3 = squareroot 2H_max/g = squareroot 2 times 309.6/9.8 s t_3 = 7.95 $ therefore t_4 = 8.36 + 7.95s therefore t_4 = 16.31 total time in air