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Use the following scenario. The Insurance Institute for Highway Safety conducts experiments in which cars are crashed into a fixed barrier at 40 mph. In a 40-mph offset test, 40% of the total width of each vehicle strikes a barrier on the driver side. The barrier's deformable face is made of aluminum honeycomb, which makes the forces in the test similar to those involved in a frontal offset crash between two vehicles of the same weight, each going just less than 40 mph. You are in the market to buy a new family car and want to know whether the distribution of head injury resulting from this offset crash is the same for large family cars, passenger vans, and midsize utility vehicles at the α\alpha=0.01 level of significance. The following data were collected from the study.

Large Family CarsHead Injury (hic)Passenger VansHead Injury (hic)Mid Size Utility VehiclesHead Injury (hic) Hyundai XG300264Toyota Sienna148Honda Pilot225Ford Taurus134Honda Odyssey238Toyota 4Runner216Buick LeSabre409Ford Freestar340Mitsubishi Endeavor186Chevrolet Impala530Mazda MPV693Nissan Murano307Chrysler 300149Chevrolet Uplander550Ford Explorer353Pontiac Grand Prix627Nissan Quest470Jeep Liberty411Toyota Avalon166Kia Sedona322Buick Rendezvous397\begin{matrix} \text{Large Family Cars} & \text{Head Injury (hic)} & \text{Passenger Vans} & \text{Head Injury (hic)} & \text{Mid Size Utility Vehicles} & \text{Head Injury (hic)}\\ \text{ Hyundai XG300} & \text{264} & \text{Toyota Sienna} & \text{148} & \text{Honda Pilot} & \text{225}\\ \text{Ford Taurus} & \text{134} & \text{Honda Odyssey} & \text{238} & \text{Toyota 4Runner} & \text{216}\\ \text{Buick LeSabre} & \text{409} & \text{Ford Freestar} & \text{340} & \text{Mitsubishi Endeavor} & \text{186}\\ \text{Chevrolet Impala} & \text{530} & \text{Mazda MPV} & \text{693} & \text{Nissan Murano} & \text{307}\\ \text{Chrysler 300} & \text{149} & \text{Chevrolet Uplander} & \text{550} & \text{Ford Explorer} & \text{353}\\ \text{Pontiac Grand Prix} & \text{627} & \text{Nissan Quest} & \text{470} & \text{Jeep Liberty} & \text{411}\\ \text{Toyota Avalon} & \text{166} & \text{Kia Sedona} & \text{322} & \text{Buick Rendezvous} & \text{397}\\ \end{matrix}


The velocity in the 2cm2-\text{cm}-diameter pipe of Fig. has only one nonzero velocity component given by u(r,t)=2(1r2/r02)(1et/10) m/su(r, t)=2\left(1-r^2 / r_0^2\right)\left(1-e^{-t / 10}\right)~\mathrm{m} / \mathrm{s}, where r0r_0 is the radius of the pipe and tt is in seconds. Calculate the maximum velocity and the maximum acceleration: (a) Along the centerline of the pipe (b) Along a streamline at r=0.5 cmr=0.5 \mathrm{~cm} (c) Along a streamline just next to the pipe wall [Hint: Let vz=u(r,t),vr=0v_z=u(r, t), v_r=0, and vθ=0v_\theta=0 in the appropriate equations in Table.]


Answered 1 year ago
Answered 1 year ago
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Given the following:

u(r,t)=2(1r2r02)(1et10)d=2 cmvz=u(r,t)vr=0vθ=0\begin{align*} u\left(r,t\right)&=2\left(1-\dfrac{r^{2}}{r_{0}^{2}}\right)\left(1-e^{\frac{-t}{10}}\right)\\\\ d&=2\ \text{cm}\\ v_{z}&=u\left(r,t\right)\\ v_{r}&=0\\ v_{\theta}&=0 \end{align*}

Determine the maximum velocity and the maximum acceleration a) along the center, b) at r=0.5 cmr=0.5\ \text{cm}, and c) next to the pipe wall.

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