In an industrial process, the sprayer in the figure shown below projects a strea

Question

In an industrial process, the sprayer in the figure shown below

projects a stream of liquid onto the horizontal surface. An

engineer wants to place the sprayer at a horizontal position, xe,

that maximizes its coverage of the horizontal surface, i.e., she

wants to maximize the distance xs – xe reached

by the spray. The angle q0 can be varied but the spray velocity v0

= 3 m/s is fixed. The dimensions H = 0.2 m, L = 0.12 m, and h =

0.06 m. If the droplets of the spray are treated as projectiles,

what is the desired position, xe? Hint: Find the angle q0 that just

clears H at xe and find xs. Plot  xs

– xe a s a function of xe and find the maximum.

Explanation / Answer

Total length of the sides added together is the perimeter. 84 in. The perimeter is all 4 sides added together, so: 2x + 5 + 3x - 2 + 3x + x = 84 add like terms 9x + 3 = 84 9x = 81 x = 81/9 x = 9 Side BC is 3(9) - 2 = 27 - 2 = 25 inches

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