When a water gun is fired while being held horizontally at a height of 1.00 m above ground level, the water travels a horizontal distance of 5.00 m. a child, who is holding the same gun in a horizontal position, is also sliding down a 45.0° incline at a constant speed of 2.00 m/s. if the child fires the gun when it is 1.00 m above the ground and the water takes 0.329 s to reach the ground, how far will the water travel horizontally?

Question

Physics

Frank

17 November, 03:52

When a water gun is fired while being held horizontally at a height of 1.00 m above ground level, the water travels a horizontal distance of 5.00 m. a child, who is holding the same gun in a horizontal position, is also sliding down a 45.0° incline at a constant speed of 2.00 m/s. if the child fires the gun when it is 1.00 m above the ground and the water takes 0.329 s to reach the ground, how far will the water travel horizontally?

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Answers (1)

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Zachary Young · Answer 1

Refer to the diagrams shown below.

Neglect air resistance.

Case A.

Let t = the time of flight.

Then for horizontal travel,

t = (5 m) / (u m/s) = 5/u s

For vertical travel,

1.0 m = (1/2) * (9.8 m/s²) * (5/u s) ²

5/u = √ (1/4.9) = 0.4518

u = 11.0668 m/s

Case B.

There are two contributions to the horizontal velocity

(i) 11.0668 m/s

(ii) (2 m/s) * cos (45) = 1.4142 m/s

The total horizontal velocity is

11.0668 + 1.4142 = 12.481 m/s

Because the time of flight is 0.329 s, the horizontal distance traveled is

d = (12.481 m/s) * (0.329 s) = 4.106 m

Answer: The horizontal distance traveled is 4.11 m