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Oksi-84 [34.3K]
3 years ago
8

A girl swings on a playground swing in such a way that at her highest point she is 4.1 m from the ground, while at her lowest po

int she is 0.8 m from the ground. What is her maximum speed?The acceleration of gravity is 9.8 m/s². Answer in units of m/s.
Physics
1 answer:
Umnica [9.8K]3 years ago
8 0

Answer:

V1 =8.1 m/s

Explanation:

height at highest point (h2) = 4.1 m

height at lowest point (h1) = 0.8 m

acceleration due to gravity (g) = 9.8 m/s^{2}

from conservation of energy, the total energy at the lowest point will be the same as the total energy at the highest point. therefore

mgh1 + 0.5mV1^{2} = mgh2 + 0.5mV2^{2}

where

  • speed at highest point = V2
  • speed at lowest point = V1
  • mass of the girl and swing = m
  • at the highest point, the  speed is minimum (V1 = 0)
  • at the lowest point the speed is maximum (V2 is the maximum speed)
  • therefore the equation becomes mgh1 + 0.5mV1^{2} = mgh2

      m(gh1 + 0.5V1^{2}) = m(gh2)

      gh1 + 0.5V1^{2} = gh2

      V1 = \sqrt{\frac{gh2 - gh1}{0.5}}

now we can substitute all required values into the equation above.

V1 = \sqrt{\frac{(9.8x4.1) - (9.8x0.8)}{0.5}}

V1 = \sqrt{\frac{32.34}{0.5}}

V1 =8.1 m/s

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The greatest speed recorded by a baseball thrown by a pitcher was 162.3 km / h, obtained by Nolan Ryan in 1974. If the ball leav
Pepsi [2]

Answer:

0.96 m

Explanation:

First, convert km/h to m/s.

162.3 km/h × (1000 m/km) × (1 hr / 3600 s) = 45.08 m/s

Now find the time it takes to move 20 m horizontally.

Δx = v₀ t + ½ at²

20 m = (45.08 m/s) t + ½ (0 m/s²) t²

t = 0.4436 s

Finally, find how far the ball falls in that time.

Δy = v₀ t + ½ at²

Δy = (0 m/s) (0.4436 s) + ½ (-9.8 m/s²) (0.4436 s)²

Δy = -0.96 m

The ball will have fallen 0.96 meters.

3 0
3 years ago
A bottle lying on the windowsill falls off and takes 4.95 seconds to reach the ground. The distance from the windowsill to the g
Liula [17]
The distance an object falls from rest through gravity is 
                        D  =  (1/2) (g) (t²) 
           Distance  =  (1/2 acceleration of gravity) x (square of the falling time)

We want to see how the time will be affected 
if  ' D ' doesn't change but ' g ' does. 
So I'm going to start by rearranging the equation
to solve for ' t '.                                                      D  =  (1/2) (g) (t²)

Multiply each side by  2 :         2 D  =            g    t²  

Divide each side by ' g ' :      2 D/g =                  t² 

Square root each side:        t = √ (2D/g)

Looking at the equation now, we can see what happens to ' t ' when only ' g ' changes:

  -- ' g ' is in the denominator; so bigger 'g' ==> shorter 't'

                                             and smaller 'g' ==> longer 't' .-- 

They don't change by the same factor, because  1/g  is inside the square root.  So 't' changes the same amount as  √1/g  does.

Gravity on the surface of the moon is roughly  1/6  the value of gravity on the surface of the Earth.

So we expect ' t ' to increase by  √6  =  2.45 times.

It would take the same bottle  (2.45 x 4.95) = 12.12 seconds to roll off the same window sill and fall 120 meters down to the surface of the Moon.
5 0
3 years ago
(1 pt) A bucket of water of mass 20 kg is pulled at constant velocity up to a platform 35 meters above the ground. This takes 14
Elenna [48]

Answer:

w = 5832.372 Joules

Explanation:

Mass of water, m = 20 kg

The water was pulled up to a height of 35 meters, i.e. h = 35 m

It takes 14 minutes to pull up the water through the height, 35 m

speed = distance/ time = 35/14 = 2.5 m/min

The bucket's height, y = speed * time = 2.5t meters

6 kg of water drips out of the bucket throughout the 14 minutes

The rate at which the water drips drips out = (6/14) = 0.4286 kg/min

Mass of water that drips out in time, t = 0.4286t kg

The mass of water remaining = (20 - 0.4286t) kg

Change in Workdone, Δw = mgΔy

Δy = 2.5 Δt

Δw = mg *  2.5 Δt

dw =  (20 - 0.4286t)g2.5 dt

integrating both sides

dw = (50g - 1.07gt)dt

w = \int\limits^a_b {(50g-1.07gt)} \, dx where b = 0, a = 14

w = 50gt - 1.07g(t²)/2      g = 9.8 m/s²

w = 490t - 5.243t²

w = (490*14 - 5.243*14²) - (490*0 - 5.243*0²)

w = 6860 - 1027.628

w = 5832.372 Joules

3 0
3 years ago
1. Indica cuáles son los reactivos y productos de la reacción química representada por la ecuación siguiente, y señala en que es
bearhunter [10]

Answer:

Los reactivos, con su correspondiente estado de agregación, son:

  • Mg: estado sólido
  • HCl: estado acuoso

Los productos, con su correspondiente estado de agregación, son:

  • MgCl₂: estado acuoso
  • H₂: estado gaseoso

Explanation:

Una reacción química es un proceso por el cual una o más sustancias se transforman en otra u otras sustancias con propiedades diferentes. En otras palabras, las reacciones químicas son procesos en los que los átomos rompen sus enlaces químicos y forman otros nuevos, cambiando la naturaleza de las sustancias que intervienen.

En una ecuación química se representan dos términos. En el primero, el de la  derecha, se escriben los reactivos, expresados mediante sus fórmulas químicas  correspondientes y separados por un signo más. Por otro lado, el término de la izquierda, en  el que aparecen los productos, también representados por sus formulas químicas  correspondientes y con signos más entre ellos. Entre ambos términos suele ponerse  una flecha que indica que se ha producido la reacción química correspondiente.

Las sustancias que hay antes de producirse el cambio y que desaparecen se llaman reactivos. Las sustancias que hay después de producirse el cambio y que aparecen o se generan se llaman productos.

El estado de agregación en una reacción química se indica poniendo detrás del nombre o la fórmula de la sustancia y entre paréntesis la notación siguiente:

  • Sustancias sólidas (s)
  • Sustancias líquidas (l)
  • Sustancias gaseosas (g)
  • Sustancias disueltas en agua (aq)

En este caso tienes la reacción química:

Mg (s) + 2 HCl (aq) -> MgCl₂ (aq) + H₂ (g)

Entonces, <u><em>en este caso los reactivos, con su correspondiente estado de agregación, son:</em></u>

  • <u><em>Mg: estado sólido</em></u>
  • <u><em>HCl: estado acuoso</em></u>

<u><em>Por otro lado, los productos, con su correspondiente estado de agregación, son:</em></u>

  • <u><em>MgCl₂: estado acuoso</em></u>
  • <u><em>H₂: estado gaseoso</em></u>

6 0
3 years ago
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