Manure Spreader
September 14th, 2011
Manure Spreader
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Manure Spreader
Mustang question with physics?
In his Mustang, Juan rounds a curve onto a straight section of country road while traveling at a speed of 17.0 m/s , only to find a fully loaded manure spreader completely blocking the road a distance 38.0 m ahead of him. Startled, he travels at a constant velocity for a period of reaction time of 0.850 s , then hits the brakes and slows at constant acceleration so that he manages to stop just short of the spreader.
With the same reaction time and acceleration, if he had roared around the corner at a speed of 28.0 m/s instead of 17.0 m/s, how fast would he have been going when he hit the spreader?
How much time would he have had for his life to flash before his eyes from the time he first sees the spreader until he hits it?
1) In the next 0.850 s Juan travels another 14.45 m, so there is 38-14.45 m = 23.55 meter left to brake.
Let a be the deceleration, then we have at t_stop
v(t)=17.0 - at = 0
x(t)=17.0 t - 0.5 at^2 = 23.55
Solve: a = 6.14 m/s^2 and t=2.77 seconds
2) In this case Juan reacts after 28 * 0.85 = 23.8 m and has 38-23.8 = 14.2 meters left to brake.
The equations are
v(t) = 28.0 - at = 28.0 - 6.14 t
x(t) = 28.0 t -0.5 at^2 = 28.0 t - 3.07 t^2
At impact we have 28.0 t - 3.07 t^2 = 14.2
Solve for t, t=0.539 seconds
v(0.539) = 24.69 m/s
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Manure Spreader
Manure Spreader
Manure Spreader, Manure Spreaders, Classic Spreader by ABI
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