Question

El caño de una fuente está inclinado 60° sobre la horizontal. Si el agua sale del caño con una velocidad inicial de 10 m/s: a) ¿Qué dibujo forma el chorro de agua? B) ¿Qué altura máxima alcanza el agua? C) ¿A qué distancia del caño hay que colocar el sumidero? D) ¿Cuál es el módulo de la velocidad del agua cuando esta cae al sumidero

Answer 1

Answer:

A) Parabola; B) 3.83 m; C) 8.84 m; D) 10 m/s

Step-by-step explanation:

A) Shape of water jet

The water jet has the shape of a parabola.

B) Maximum height

Data:

θ = 60°

u = 10 m/s

a = 9.8 m·s⁻²

Calculations:

1. Calculate the horizontal and vertical components of the velocity

$u_{\text{h}} = u \cos \theta = \text{10 m/s} \times \cos 60 ^{\circ} = \text{10 m/s} \times 0.5 = \text{5 m/s}\\u_{\text{v}} = u \sin \theta = \text{10 m/s} \times \sin 60 ^{\circ} = \text{10 m/s} \times 0.866 = \text{8.66 m/s}$

2. Maximum height

$H = \dfrac{(u_{\text{v}})^{2}}{2a} = \dfrac{8.66^{2}}{2\times 9.8} =\textbf{3.83 m}$

C) Range

1. Calculate the time of flight

Use the vertical component of velocity to calculate the time to the maximum height of the stream.

$u_{\text{v}} = at\\t = \dfrac{ u_{\text{v}}}{a} = \dfrac{\text{8.66 m \cdot s}^{-1}}{\text{9.8 m \cdot s}^{-2}}= \text{0.884 s}$

It will take the same time to reach the ground.

Thus,

Time of flight = 2t = 2 × 0.884 s  = 1.77 s

2. Calculate the horizontal distance

s = vt = 5 m·s⁻¹ × 1.77 s = 8.84 m  

You should place the drain 8.84 m from the pipe.}

D) Modulus of velocity

The stream of water will hit the drain with the same velocity as when it left the pipe.

Thus, the modulus of the velocity is 10 m/s.

The graph below shows the trajectory of the water stream.