question in the picture **Pulley System Problem**You need to lift a very heavy pile of bricks to a second story window. You fix a pulley 30 ft high. A rope connects the bricks to your truck through the pulley. The truck starts right beneath the pulley and slowly drives away from the bricks at a rate of 3 ft per second to lift the bricks._See diagram for reference._**Diagram Explanation:**A pulley is mounted 30 feet above the ground. A truck is positioned directly below the pulley. A rope runs from a pile of bricks, up to the pulley, and then to the truck. As the truck moves horizontally, the bricks are lifted off the ground.**Questions:**(a) After 4 seconds, how fast is the angle θ between the bricks and the truck growing?(b) After 4 seconds, how fast is the diagonal distance from the truck to the pulley growing?(c) After 4 seconds, how fast are the bricks rising in the air?

Analyze the following diagram. a) The angle between the truck and bricks can be found as, Here, H and x represent the pully’s height and distance moved by truck, respectively. The rate at which the angle is growing can be found by differentiating both the sides with time, Here, s represents the truck’s speed. The distance moved by the truck after 4 s can be found as, Here, t represents the time taken to move this distance. Substitute the relevant values. Now, the angle between the truck and bricks can be found as, Substitute the relevant values. Substitute the relevant values in equation (1). Thus, the angle is growing at a rate of 0.086 degrees per second. b) The diagonal distance between the truck and pully can be represented as, The rate of change of the diagonal can be found as, After 4 s, the diagonal distance can be found as, Substitute the relevant values in equation (2). Thus, the rate at which the diagonal distance grows is 1.11 ft/s. c) The length of the rope is constant at any time it can be given as, Here, L and l represent the rope’s total length and length of the rope from pulley to the bricks, respectively. Differentiating both sides with time. Substitute the relevant values. Thus, the bricks are rising at a rate of 1.11 ft/s.