Directions: Answer ALL parts. Show all work and please write neatly.

A crane and box are both initially at rest. At time t=0 s, the crane begins to drive forward at a constant speed of 0.5 m/s, while also lifting the box with an upward acceleration of 1 m/s2. The box does not swing while being lifted by the crane.

part a) Draw the path the block would take as it moves with constant velocity in the horizontal direction, as it accelerates upwards.

part b) Sketch the shape of the path taken by the box as it is lifted by the crane as viewed by a stationary observer. Justify the shape of the path you drew above.

part c) Assume that, at t=0s, 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.

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

At time t=t1, the crane begins to accelerate forward, reaching a new constant velocity at time t=t2. The box accelerates upwards during the entire time interval t1

part e) The dot below represents the box during the time interval t1