As Spif the longboarder approaches bottom of the
hill his situation looks dire as detailed in the diagram.
Furiously racking his brain over a matter of nanoseconds he tries to think of a way to use the enemy of sick speed Friction to his advantage. He remembers watching a video explaining how to do a standing board slide. Realizing he has only moments to make a decision he decides to simply go for it.
Remembering the video's instructions to simply lean back and turn his board to 90º to his current vector velocity he gets into position to begin his slide just as he meets the bottom of the hill 75m away from the catastrophe.
Furiously racking his brain over a matter of nanoseconds he tries to think of a way to use the enemy of sick speed Friction to his advantage. He remembers watching a video explaining how to do a standing board slide. Realizing he has only moments to make a decision he decides to simply go for it.
Remembering the video's instructions to simply lean back and turn his board to 90º to his current vector velocity he gets into position to begin his slide just as he meets the bottom of the hill 75m away from the catastrophe.
Despite Spif's previously flawless
knowledge of uninteresting details relating to a hill
and it's conditions he forgets what type of longboard
wheels he put on today. Miraculously he forgets his
rapid approach towards the explosive truck and instead
begins to think about a way to tell if he installed his
80a polyurethane wheels or kept his 60a polyurethane
wheels from yesterday on.
Thankfully his encyclopedia of a brain comes to the rescue once again he remembers the coefficients of friction for his two sets of wheels. His 60a wheels he remembered were softer than his 80a wheels and they had a kinetic coefficient of friction on asphalt of μk = .8 and his kinetic coefficient of friction for his 80a wheels on asphalt was μk = .6 (Spif assumes a velocity of 31.31m/s with his mass systems of 100kg is enough to overcome static friction)
Since Spif is now on a flat surface he knows gravity will not accelerate him any more leaving friction as the only force affecting his velocity.
To clear his mind Spif lays out the formulas needed to calculate the distance he will travel.
Thankfully his encyclopedia of a brain comes to the rescue once again he remembers the coefficients of friction for his two sets of wheels. His 60a wheels he remembered were softer than his 80a wheels and they had a kinetic coefficient of friction on asphalt of μk = .8 and his kinetic coefficient of friction for his 80a wheels on asphalt was μk = .6 (Spif assumes a velocity of 31.31m/s with his mass systems of 100kg is enough to overcome static friction)
Since Spif is now on a flat surface he knows gravity will not accelerate him any more leaving friction as the only force affecting his velocity.
To clear his mind Spif lays out the formulas needed to calculate the distance he will travel.
To find the distance traveled
Vf ^2 =Vi^2 + 2aΔx
Vf is assumed to be 0 and Vi is known to be 31.31m/s so....
0 =(31.31m/s)^2 + 2aΔx
Using basic algebra he finds
-490.15/a = Δx
To find his acceleration
a = -μk * g
For the two different coefficients the equations are as follows
a(60a) = -.8 * 9.8 = -7.84m/s
a(80a) = -.6 * 9.8 = -5.88m/s
So as Spif continues his slide he finds that
Δx(60a) = -490.15 / -7.84m/s = 62.52m
and
Δx(80a)= -490.15 / -5.88m/s = 83.37m
Vf ^2 =Vi^2 + 2aΔx
Vf is assumed to be 0 and Vi is known to be 31.31m/s so....
0 =(31.31m/s)^2 + 2aΔx
Using basic algebra he finds
-490.15/a = Δx
To find his acceleration
a = -μk * g
For the two different coefficients the equations are as follows
a(60a) = -.8 * 9.8 = -7.84m/s
a(80a) = -.6 * 9.8 = -5.88m/s
So as Spif continues his slide he finds that
Δx(60a) = -490.15 / -7.84m/s = 62.52m
and
Δx(80a)= -490.15 / -5.88m/s = 83.37m
As he finalizes his calculations he
gasps. Spif realizes that since the truck was only
75m away from the bottom of the hill if he
is currently using his 80a he will momentarily be
consumed by the raging inferno that was once a
truck.
He closes his eyes and accepts his fate as he skids to a stop approximately 12.48m (75m - 62.52m = 12.48m) away from the blaze.
Spif breathes a sigh of relief and begins to ponder how convenient the use of momentum is for taking him home.
He closes his eyes and accepts his fate as he skids to a stop approximately 12.48m (75m - 62.52m = 12.48m) away from the blaze.
Spif breathes a sigh of relief and begins to ponder how convenient the use of momentum is for taking him home.