Question

The figure shows a stream of water flowing through a hole at depth h = 9.66 cm in a tank holding water to height H = 31.1 cm. (a) At what distance x does the stream strike the floor? (b) At what depth should a second hole be made to give the same value of x? (c) At what depth should a hole be made to maximize x?

Answer 1

a) By Bernoulli's eq", at the top surface & at the holes Rote gh = 8 + Isuz i v = 2gh Now water steam falls down a vertical distance H-h before hitting the foor. The time of flight is given by H-h - gt? = gt2 = t = |26H-h) t Vg 1 The motion of ejected water is a projectile motime - horizontal displacement as is given by x = vt - J2gh 12(H-b) 2 VHh-h2 - 0 X = 2 31.1x9.66- 9.662 = x = 28.8 cm b) giving Let the the same depth of value new hole is h. of x ase h, we For get 2/Hb-h2 = 2 JHh-h2 : Hh-h2= Hhah'2 > h² h² + Hh - Hhoto is (b? + b – H) ( h-h) = 0 → hah, H-h : b- H-h - 31.1- 9.66 This 21.44 cm

c) We have x=2 VHb-h2 x, f(h) = H h h2 should be To maximize maximum. & f(h) = Hh-ha takes maximum value at a point where its first derivative is zero - f'(h) = 0 H - 2 h = 0 + > b. . 3.1;! . h - 15. 55 cm