Answer:
The area of the water stream will be 1.74 cm^2
Explanation:
initial velocity of water u = 33.2 cm/s
initial area = 6.4 cm^2
height of fall = 7.05 cm
final area before hitting the sink = ?
as the water falls down the height, it accelerates under gravity; causing the speed to increase, and the area to decrease.
first we find the velocity before hitting the sink
using
[tex]v^{2} = u^{2} + 2gh[/tex] -----Newton's equation of motion
where v is the velocity of the water stream at the sink
u is the initial speed of the water at the spout
h is the height of fall
g is acceleration due to gravity, and it is positive downwards.
g = 981 cm/s^2
imputing relevant values, we have
[tex]v^{2} = 33.2^{2} + (2 * 981 * 7.05)[/tex]
[tex]v^{2} = 1102.24 + 13832.1 = 14934.34[/tex]
[tex]v = \sqrt{14934.34}[/tex] = 122.206 cm/s
according to continuity equation,
A1v1 = A2v2
where A1 is the initial area
V1 = initial velocity
A2 = final area
V2 = final velocity
6.4 x 33.2 = 122.206 x A2
212.48 = 122.206 x A2
A2 = 212.48 ÷ 122.206 ≅ 1.74 cm^2
