Respuesta :
Answer:
The time that elapses before the players collide is 4.59 secs
Step-by-step explanation:
The distance between the two players is 41 meters. Hence, they would have total distance of 41 meters by the time they collide.
We can write that
S₁ + S₂ = 41 m
Where S₁ is the distance covered by Player 1 before collision
and S₂ is the distance covered by Player 2 before collision
From one of the equations of kinematics for linear motion,
[tex]S = ut[/tex] + [tex]\frac{1}{2} at^{2}[/tex]
Where [tex]S[/tex] is distance
[tex]u[/tex] is the initial velocity
[tex]a[/tex] is acceleration
and [tex]t[/tex] is time
Since the players collide at the same time, then time spent by player 1 before collision equals time spent by player 2 before collision
That is, t₁ = t₂ = t
Where t₁ is the time spent by player 1
and t₂ is the time spent by player 2
For player 1
[tex]S[/tex] = S₁
[tex]u[/tex] = 0 m/s ( The player starts at rest)
[tex]a[/tex] = 2.2 m/s²
Then,
S₁ = [tex]0(t)[/tex] + [tex]\frac{1}{2} (2.2)t^{2}[/tex]
S₁ = [tex]1.1t^{2}[/tex]
[tex]t^{2} = \frac{S_{1} }{1.1}[/tex]
For player 2
[tex]S[/tex] = S₂
[tex]u[/tex] = 0 m/s ( The player starts at rest)
[tex]a[/tex] = 1.7 m/s²
Then,
S₂ = [tex]0(t)[/tex] + [tex]\frac{1}{2} (1.7)t^{2}[/tex]
S₂ = [tex]0.85t^{2}[/tex]
[tex]t^{2} = \frac{S_{2} }{0.85}[/tex]
Since the time spent by both players is equal, We can write that
[tex]t^{2}[/tex] = [tex]t^{2}[/tex]
Then,
[tex]\frac{S_{1} }{1.1} = \frac{S_{2} }{0.85}[/tex]
[tex]0.85S_{1} = 1.1S_{2}[/tex]
From, S₁ + S₂ = 41 m
S₂ = 41 - S₁
Then,
[tex]0.85S_{1} = 1.1 ( 41 -S_{1} )[/tex]
[tex]0.85S_{1} = 45.1 - 1.1S_{1}[/tex]
[tex]0.85S_{1} + 1.1S_{1} = 45.1 \\1.95S_{1} = 45.1\\S_{1} = \frac{45.1}{1.95} \\S_{1} = 23.13 m[/tex]
This is the distance covered by the first player. We can then put this value into [tex]t^{2} = \frac{S_{1} }{1.1}[/tex] to determine how much time elapses before the players collide.
[tex]t^{2} = \frac{S_{1} }{1.1}[/tex]
[tex]t^{2} = \frac{23.13 }{1.1}[/tex]
[tex]t^{2} = 21.03\\t = \sqrt{21.03} \\t = 4.59 secs[/tex]
Hence, the time that elapses before the players collide is 4.59 secs
