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A child, starting from rest at the top of a playground slide, reaches a speed of 7.0 meters per second at the bottom of the slide. what is the vertical height of the slide? [neglect friction.]

Respuesta :

W0lf93
We know that the child will follow a accelerated movement due the gravity, according these equations:  
h = v0 * t + 1/2 * g * t^2  
v = v0 + g*t  
where h is height, v is final speed, v0 is initial speed, g is gravity constant equal to 9.8 m/s2 and t is time  
So the time to reach the bottom of the slide 
v = v0 + g*t => 7 = 0 + 9.8*t  
t = 7/9.8 = 0.714 seconds 
 And then the height is: 
h = v0*t + 1/2*g*t^2 
h = 0*0.714 + 1/2*9.8*0.714^2 = 2.5 meters  
So the height of the slide is 2.5 meters
snehashish65

The vertical height achieved by child during sliding is 2.50 m

Given data:

The initial speed of child is, u = 0 m/s. (Since child was initially at rest)

The final speed of child is, v = 7 m/s.

Apply first kinematic equation of motion to obtain the value of time (t) to achieve the vertical height (h) as,

[tex]v=u+gt[/tex]

Here, g is the gravitational acceleration.

Solving as,

[tex]7.0=0+(9.8)t\\t=0.714 \;\rm s[/tex]

Now, apply the second kinematic equation of motion as,

[tex]h=ut+\dfrac{1}{2}gt^{2}\\\\h=(0 \times t) +\dfrac{1}{2} \times 9.8 \times 0.714^{2}\\h \approx 2.50 \;\rm m[/tex]

Thus, we can conclude that the vertical height of the slide is 2.50 m.

Learn more about kinematic equations of motion here:

https://brainly.com/question/16995301

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