Chapter 3, Problem 3.40P

CALC A faulty model rocket moves in the xy-plane (the positive y-direction is vertically upward). The rocket’s acceleration has components a_x(t) = αt² and a_y(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 ${\stackrel{\to }{\upsilon }}_0={\upsilon }_{0x}\hat{i}+{\upsilon }_{0y}\hat{j}$ with υ_0x = 1.00 m/s and υ_0y = 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) What is the horizontal displacement of the rocket when it returns to y = 0?