Water flowing through a 1.6-cm-diameter pipe can fill a 500 L bathtub in 6.5 min. What is the speed of the water in the pipe?

The speed of the water is "12.95 m/s".

According to the question,

Volume,

           =

Time,

          =

          =

Diameter,

           = 0.016 m

As we know,

Area of cross-section of pipe will be:

→

Flow rate is:

→

Thus the above approach is right.          

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v = 6.38 m/s

Explanation:

discharge Q = 500 L / 6.5 min

flow through pipe is 1.6 cm x (1 m/100 cm ) = 0.016 m

using the flow rate formula Q = A * v

where A = area, v = velocity

the speed of water in the pipe = v = Q / A

      500 L        1 m³          1 min           π (0.016 m)²

v =   x    x    ÷  

      6.5 min       10³ L       60 sec                 4

v = 6.38 m/s

air exerts forces on falling objects near earth’s surface.

explanation:

the term 'free falls' refer to object that are falling towards the earth, in a situation in which gravity is the only force acting on the object.

for an object in free fall, the acceleration is constant (g, the gravitational acceleration), and so the velocity of the object constantly increases.

for objects near earth's surface, there is always another force acting on the object: the resistance due to the air. this force is opposed to the direction of fall of the object, and it is proportional to the velocity of the object, so as the object falls down, this force increases up to a point when it balances the force of gravity, and the object continues its motion at constant velocity (called terminal velocity). since in this case gravity is not the only force acting on the object, we are not in a situation of free fall.