Question

A dam holds back the water in a lake. If the dam has a small hole 1.4 meters below the surface of the lake, at what speed does water exit the hole?

A.8.2 m/s
B.7.2 m/s
C.6.2 m/s
D.5.2 m/s

Answer 1

The speed at which water exits the hole in the dam, 1.4 meters below the surface of the lake, can be determined by Torricelli's Law, a simplification of Bernoulli's equation, giving us a speed of 5.2 m/s.

Step-by-step explanation:

To find the speed at which water exits the hole in the dam, we can use the principle of Bernoulli's equation which, in this case, simplifies to Torricelli's Law. The law states that the speed (v) of a fluid flowing out of an opening in a tank is equivalent to that of an object falling freely from the same height (h) in a gravitational field, given by the equation v = √(2gh) where g is the acceleration due to gravity (9.8 m/s²) and h is the depth below the surface (1.4 m in this case).

If we plug in the numbers, we get:

v = √(2 × 9.8 m/s² × 1.4 m) = √(27.44 m²/s²) = 5.2 m/s

Therefore, the correct answer is D. 5.2 m/s.