25 points Water flows from a drain spout at an angle 15 belo

(25 points) Water flows from a drain spout at an angle 15° below horizontal as shown in the figure. If the bucket is placed a distance, d- 8 ft from the wall, determine the range of values for the initial velocity, Vo, of the water, such that the water will enter the bucket. 1. 10 ft 1.2 ft 2 ft

Solution

Concept: Using the equations of projectile motion the range of values of velocity could be obtained.

Water is said to have entered the bucket if it either enters the left end of the bucket or enters the right end of the bucket and enters the top edge of the bucket.

Using x = u_xt and y= u_yt+1/2gt² where x and y are the distances covered in x and y direction respectively, u_x and u_y are the velocities in x and y direction respectively, t is the time taken to cover the distance.

Case1) When water enters the left end of the bucket

8 = v₀cos15 t

8.8 = v₀sin15t+1/2gt²

Substituting the value of t from the first equation we obtain

8.8 = 8 tan15+1103.49/(v₀)² (g=32.174 ft/s²⁾

Hence v₀ = 12.87 ft/s.

Case 2)When water enters the right end of the bucket

10= v₀cos15 t

8.8 = v₀sin15t+1/2gt²

Substituting the value of t from the first equation we obtain

8.8 = 10tan15+1724.2/(v₀)² (g=32.174 ft/s²⁾

Hence v₀ = 16.78 ft/s.

Hence the range of values for the initial velocity of water is between 12.87ft/s and 16.78ft/s.