Respuesta :
Answer:
2.93 s
Explanation:
Given that,
Initial speed of the Cheetah is, [tex]u = 1.15 m / s[/tex]
distance has to be covered by Cheetah, [tex]S= 43 m[/tex]
Acceleration of the Cheetah is, [tex]a= 9.25 m/s^{2}[/tex]
From the second equation of motion,
[tex]S = ut + ( 1/ 2) at ^ 2[/tex]
Therefore,
[tex]43 = 1.15 t + 4.625 t ^ 2\\4.625 t ^ 2 + 1.15 t -43 = 0[/tex]
Therefore,
[tex]t =\frac{ ({ -1.15\pm\sqrt{[ 1.15^ 2 - 4(4.625)(-43)}] })}{2( 4.625)}\\[/tex]
[tex]t=\frac{-1.15\pm28.24}{2\times 4.625}[/tex]
Now only consider positive value of t.
[tex]t=\frac{-1.15+28.24}{2\times 4.625}\\=2.93s[/tex]
Therefore the time taken by Cheetah to reach the gazelle is 2.93 s.
The time of cheetah to reach the gazelle obtained with distance formula of second equation of motion. The the time taken by the cheetah to teach te gazelle if gazelle does not move, is 2.9 seconds.
What is second equation of motion?
The second equation of motion gives the distance formula, which is used to find the distance when the acceleration and time given.
It can be given as,
[tex]s=ut+at^2[/tex]
Here, [tex]u[/tex] is the initial velocity, [tex]a[/tex] is the acceleration and [tex]t[/tex] is the time taken.
Given information-
The speed of the cheetah is 1.15 m/s.
The distance of cheetah and gazelle is 43 m.
The acceleration of the cheetah is 9.25 m/s squared.
The movement of the gazelle is zero.
As the initial velocity is 1.15 second of the cheetah. Thus put the values in the distance formula of the second equation of motion as,
[tex]43=1.15t+4.625t^2\\t=2.9\rm s[/tex]
Hence, the time taken by the cheetah to reach te gazelle if gazelle does not move, is 2.9 seconds.
Learn more about the second equation of motion here;
https://brainly.in/question/2777385
