Respuesta :
Answer:
- The ball will be strike at the ground in 15.98s.
Explanation:
Given that
- a ball is thrown directly downward with an initial speed of 8.35 m/s from a height of 29.6 m.
To find
- what time interval does it strike the ground ?
So, according the question
We have,
- Initial speed [tex]u_i = 8.35 m/s[/tex]
- Initial Height [tex]y_i = 29.6m[/tex]
The formula for the ball's height as a function of time is
[tex]y_f = y_i - u_it - \frac{1}{2} gt^2[/tex]------------------(1)
where,
[tex]y_f = final \;height=0\\y_i = initial \;height=29.6m\\u_i = initial \;velocity=8.35m/s\\\;\; g = acceleration \;due\; to\; gravity= 9.81m/s^2[/tex]
Now, putting the all given values ,
[tex]y_f = y_i - u_it - \frac{1}{2} gt^2[/tex]------------------(1)
[tex]0 = 29.6 - 8.35t - \frac{1}{2} \times9.81t^2[/tex]
or,
[tex]9.81t^2 + 16.7t -59.2 = 0\\\\t = \frac{-16.7 \pm \sqrt{(16.7)^2-4\times 9.81\times (-59.2)}}{2}}\\t = \frac{-16.7 \pm \sqrt{278.89+4\times 9.81\times 59.2}}{2}}\\t = \frac{-16.7 \pm \sqrt{278.89+2087.57}}{2}}\\t = \frac{-16.7 \pm \sqrt{2366.46}}{2}}\\t = \frac{-16.7 \pm 48.65}{2}}\\now \; we \; know \; that\; time\;always \; in\;only\;positive\\so,\\t = \frac{-16.7 + 48.65}{2}\\t = \frac{31.95}{2}\\t = 15.98s[/tex]
Answer:
- The ball will be strike at the ground in 15.98s.
To learn more about Free fall please click on link
https://brainly.com/question/13299152
#SPJ4
