A crane and box are both initially at rest. At time t=0s, the crane begins to drive forward at a constant speed of 0.5ms, while also lifting the box with an upward acceleration of 1ms2. The box does not swing while being lifted by the crane.

(c) Assume that, at t=0   s, the horizontal position of the box is x=0 and it has a vertical position of y=0. Derive an equation that describes the vertical position y of the box as a function of the horizontal position x of the box.

(d) Does your equation from part (c) agree with your sketch in part (b)? Justify your response.