It takes 2.5 minutes to fill a gas tank with 50 liters of gasoline.If the pump nozzle is 2.0 cm in radius,what is the average speed of the gasoline as it leaves the nozzle? (1 000 liters = one cubic meter)
A) 2.7 m/s
B) 0.3 m/s
C) 15.9 m/s
D) 1.3 m/s
E) 20 m/s

Question

It takes 2.5 minutes to fill a gas tank with 50 liters of gasoline.If the pump nozzle is 2.0 cm in radius,what is the average speed of the gasoline as it leaves the nozzle? (1 000 liters = one cubic meter)
A) 2.7 m/s
B) 0.3 m/s
C) 15.9 m/s
D) 1.3 m/s
E) ​20 m/s

Quizplus · Accepted Answer

We can use the equation for the flow rate of a liquid through a circular opening: Q = Av, where Q is the flow rate, A is the cross-sectional area of the opening, and v is the velocity of the liquid. We know that the volume of gasoline that flows through the nozzle in 2.5 minutes is 50 L = 0.05 m^3. We can convert the radius of the nozzle from cm to m: r = 0.02 m. The cross-sectional area of the opening is then A = πr^2 = 1.2566 x 10^-3 m^2. Using the given time and volume, we can find the flow rate: Q = 0.05 m^3 / 2.5 min = 0.00083333... m^3/s. Solving for v, we get v = Q / A = 0.6628... m/s. Rounding to one significant figure gives v = 0.7 m/s, which is closest to choice B, 0.3 m/s.

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