In a study of head injury against the instrument panel of a car during sudden or crash stops where lap belts without shoulder straps or airbags are used, the segmented human model shown in the figure is analyzed. The hip joint O is assumed to remain fixed relative to the car, and the torso above the hip is treated as a rigid body of mass m freely pivoted at O. The center of mass of the torso is at G with the initial position of OG taken as vertical. The radius of gyration of the torso about O is k_O. If the car is brought to a sudden stop with a constant deceleration a, determine the speed v relative to the car with which the model’s head strikes the instrument panel. Substitute the values m = 50 kg, r̅ = 450 mm, r = 800 mm, k_O = 550 mm, θ = 45°, and a = 10g and compute v.

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