The construction of a water pistol is shown in the figure below. The cylinder with cross-sectional area A, is filled with water and when the piston is pushed (by pulling the trigger), water is forced out the tube with cross-sectional area A₂. The radius of the cylinder and tube are, respectively, 1.20 cm and 1.50 mm, and the center of the tube is a height h = 3.00 cm above the center of the cylinder. (Assume atmospheric pressure is 1.013 x 105 Pa.) A₂ A₁ the F (a) If the pistol is fired horizontally at a height of 1.10 m, determine the time interval (in s) required for water to travel from the nozzle to the ground. Neglect air resistance. S (b) If the desired range of the stream is 7.50 m, with what speed v₂ (in m/s) must the stream leave the nozzle? m/s (c) At what speed v₁ (in m/s) must the plunger be moved to achieve the desired range? m/s

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The construction of a water pistol is depicted in the figure. The cylinder with cross-sectional area \( A_1 \) is filled with water, and when the piston is pushed (by pulling the trigger), water is forced out through the tube with cross-sectional area \( A_2 \). The radius of the cylinder and tube are 1.20 cm and 1.50 mm, respectively, and the center of the tube is at a height \( h = 3.00 \) cm above the center of the cylinder. (Assume atmospheric pressure is \( 1.013 \times 10^5 \) Pa.)

**Diagram Explanation:**

- A diagram of a water pistol is shown with labels.
- The cylinder is marked with \( A_1 \), where the plunger moves with speed \( v_1 \).
- The nozzle is marked with \( A_2 \), where water exits with speed \( v_2 \).
- The force \( \mathbf{F} \) is shown acting on the plunger.
- An arrow indicates the direction of water flow from the nozzle.

**Questions:**

(a) If the pistol is fired horizontally at a height of 1.10 m, determine the time interval (in s) required for water to travel from the nozzle to the ground. Neglect air resistance.
- Answer: ______ s

(b) If the desired range of the stream is 7.50 m, with what speed \( v_2 \) (in m/s) must the stream leave the nozzle?
- Answer: ______ m/s

(c) At what speed \( v_1 \) (in m/s) must the plunger be moved to achieve the desired range?
- Answer: ______ m/s

(d) What is the pressure (in Pa) at the nozzle?
- Answer: ______ Pa

(e) Find the pressure (in Pa) needed in the cylinder.
- Answer: ______ Pa

(f) Calculate the force (in N) that must be exerted on the trigger to achieve the desired range. (The force that must be exerted is due to pressure over and above atmospheric pressure. Enter the magnitude.)
- Answer: ______ N
Transcribed Image Text:The construction of a water pistol is depicted in the figure. The cylinder with cross-sectional area \( A_1 \) is filled with water, and when the piston is pushed (by pulling the trigger), water is forced out through the tube with cross-sectional area \( A_2 \). The radius of the cylinder and tube are 1.20 cm and 1.50 mm, respectively, and the center of the tube is at a height \( h = 3.00 \) cm above the center of the cylinder. (Assume atmospheric pressure is \( 1.013 \times 10^5 \) Pa.) **Diagram Explanation:** - A diagram of a water pistol is shown with labels. - The cylinder is marked with \( A_1 \), where the plunger moves with speed \( v_1 \). - The nozzle is marked with \( A_2 \), where water exits with speed \( v_2 \). - The force \( \mathbf{F} \) is shown acting on the plunger. - An arrow indicates the direction of water flow from the nozzle. **Questions:** (a) If the pistol is fired horizontally at a height of 1.10 m, determine the time interval (in s) required for water to travel from the nozzle to the ground. Neglect air resistance. - Answer: ______ s (b) If the desired range of the stream is 7.50 m, with what speed \( v_2 \) (in m/s) must the stream leave the nozzle? - Answer: ______ m/s (c) At what speed \( v_1 \) (in m/s) must the plunger be moved to achieve the desired range? - Answer: ______ m/s (d) What is the pressure (in Pa) at the nozzle? - Answer: ______ Pa (e) Find the pressure (in Pa) needed in the cylinder. - Answer: ______ Pa (f) Calculate the force (in N) that must be exerted on the trigger to achieve the desired range. (The force that must be exerted is due to pressure over and above atmospheric pressure. Enter the magnitude.) - Answer: ______ N
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