Question

Chapter 14 Problem 071 The figure shows a stream of water flowing through a hole at depth - 7.74 cm in a tank holding water to height second hoe be made to give the same value of (c) At what depth should a hole be made to maximize -35.7 cm. (a) At what distance x does the stream strike the floor? (b) At what depth should a Units (a) Number (b) Number (c) Number Units Units Question Attempts of used SAVE POR LATER SAHIT ANSWER

Answer 1

ay By Torricelli's low, the Velowity of the weater coming out of the hole is given by : v v=J2gh ( This is obtained by equating the sinetic energy of a water molecule of mess m, mu? to the loss in potential energy, mgh 4 solving for og When the weeter comes out of the hole, it has no initial y veloung. - using the kinematic equation for a falling body. - 4 = %ot uyt adott O = 14-h) +0 -tet t 2 (Hah) V7 horizontal distance travelled in this time is: * = + - 423 • •(---) - 2 / ACH - A) VI i fog ho7.74 cm, 4 = 35.7 cm, x=2 / 7.74 (35077.74) = 29.42cm x = 29.42 cm ] ..Ang mas I cbs we got: x=2Vhcthy - x² =4hch-h) = 4thuhe

. Lehen with tapo ih=4H I JIGH² - 16 x² 2x4 Tha HIV142 x2 2 put x =2&hicha hil ; ha = 7.74 cm h = ht ✓ 1² Ghalhah) = H I Viq2- 41+ho+Ghite H + V14 - 260)2- s h = H £ (H-2h) h = 14 +14-2hi or ha 14-4+2ha h = t-hi or hohi haha is the first hole. second hole is at depth hostahi he = 35.7 cm - 7.74 cm = 27.16 cm 7. ha = 27.96 cm] i. second hole should be made at h= 27.96 cm to give the same value of a. I ces we have: x=2&h (Hah) ..dx = 2* [CH-) + hlull] s (Hram 2/hchhi /h (th)

e hun zo gives, 14-2h Do =) ha at this h, a value of ae is maximun because minimum is zero when hat lih = 35.7 = gesam 2 i Hole should be made at to maximize a... h= 17.85 cm