A faulty model rocket moves in the xy-plane (the positive y direction is vertically upward). The rocket's acceleration has components ax (t) = αt2 and ay (t) = β - γt, where α = 2.50 m/s4, β = 9.00 m/s2, and γ = 1.40 m/s3. At t = 0 the rocket is at the origin and has velocity ~v0 = v0x ˆi + v0y ˆj with v0x = 1.00 m/s and v0y = 7.00 m/s. (a) Calculate the velocity and position vectors as functions of time. (b) What is the maximum height reached by the rocket? (c) Sketch the path of the rocket. (d) What is the horizontal displacement of the rocket when it returns to y = 0?
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