Respuesta :
The water balloon that is dropped by the student 10 meters above the ground, will hit the ground after 1.0s of falling (in 1.4 s).
To find the time we need to use the equation that related the time with the height and the acceleration due to gravity, that is to say, the first equation from the two given, but in the vertical direction:
[tex] y_{f} = y_{0} + v_{0}t + \frac{1}{2}at^{2} [/tex] (1)
Where:
[tex] y_{f}[/tex]: is the final height = 0
[tex] y_{0}[/tex]: is the initial height = 10 m
[tex] v_{0}[/tex]: is the initial velociy = 0 (it is dropped)
a: is the acceleration due to gravity = -9.8 m/s² (it is negative because its direction of motion is downward)
t: is the time =?
Solving equation (1) for t, we have:
[tex] 0 = 10 m - \frac{1}{2}gt^{2} [/tex]
[tex] t = \sqrt{\frac{2*10 m}{9.8 m/s^{2}}} = 1.4 s [/tex]
Therefore, the ballon will hit the ground after 1.0s of falling.
We used the first given equation but in the y-direction, because the equation x=x₀+v₀t+(1/2)at², considers a motion in the horizontal direction, and the ball is falling (y-direction). We did not use the other equation (v = v₀ + at) because we do not know the final velocity of the ball before it hits the ground (v).
You can see another example of free fall here: https://brainly.com/question/13344403?referrer=searchResults
I hope it helps you!
Answer:
The time it takes for the balloon to hit the ground is 1.4 seconds. So the answer is the balloon would hit the ground after 1.0 s of falling.
Explanation:
The answer can be found by using the equation [tex]x=x_{0}+v_{0}t+\frac{1}{2}at^{2}[/tex]
The first step is to identify what each value is and the information we are provided with:
x is the position; the balloon falls to the ground, so [tex]x = 0[/tex]
x0 is the initial position; the balloon is 10 meters high, so [tex]x_{0} = 10[/tex]
t is the time; we are solving for time
a is the acceleration; in this case it is gravity (9.8 m/s^2), so [tex]a = 9.8[/tex]
*we do not need v0, or initial velocity, for this problem
The next step is to input the information into the equation:
the equation now looks like this [tex]0=10-(\frac{1}{2}9.8)t^{2}[/tex]
**because the acceleration is gravity and the balloon is falling downwards, the acceleration becomes negative (-9.8 m/s^2)
Steps to solving this equation:
1) multiply 9.8 by 1/2 inside the parenthesis
[tex]0=10-(\frac{1}{2}9.8)t^{2}[/tex]
[tex]0=10 -(4.9)t^{2}[/tex]
[tex]0=-4.9t^{2} + 10[/tex]
2) add 4.9t^2 to both sides of the equation
[tex]4.9t^{2} = 10[/tex]
3) divide both sides by 4.9
[tex]\frac{4.9t^{2}}{4.9}= \frac{10}{4.9}[/tex]
[tex]t^{2} = 2.040816[/tex]
4) find the square root
[tex]\sqrt{t} = \sqrt{2.040816}[/tex]
[tex]t=1.4[/tex]
This is how we can use the equation [tex]x=x_{0}+v_{0}t+\frac{1}{2}at^{2}[/tex] to find the answer 1.4 seconds.
the balloon hits the ground after falling for 1.4 seconds.
