Yellow Banana Tracy Lynn was a third year medical student at Municipal Medical S

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Yellow Banana Tracy Lynn was a third year medical student at Municipal Medical School in Gotham City. She was in her last week of a rotation in the shock-trauma unit. She was leaving for a weekend trip to visit her boyfriend when her supervising resident physician, Dave, warned her (as he did every weekend), "Drive carefully. I don't want to see you in one of these beds when I come in on Monday!" Tracy had always been a careful driver, but since working in shock trauma she had seen the and seat belts gave to car accident victims. Dave always told her that air bags protected people devastating results of car accidents. In particular, she had come to see the protection that air bags much more that just seat belts alone. Question: your answer using physics principles. Tracy was on Highway 51 headed east out of town when, out of the corner of her eye she noticed Why are air bags (with lap and shoulder straps) safer than lap and shoulder straps alone? Justify a white car hesitate, then start across the road in front of her. She slammed on her brakes in an attempt to avoid a collision, however she was too late! Her 1972 Pontiac LeMans (affectionately known as the "yellow banana"), weighing 4300 lbs, broadsided the white Buick Century, weighing 3100 lbs. When the cars finally came to a stop, Tracy took inventory of herself and except for a very sore chest (where the shoulder strap was positioned) and neck, she was shakern but OK. Tracy got out of her car to check on the driver of the white car. Unfortunately, the other driver was barely conscious, having been thrown against the side window and door of the car She was not wearing a seat belt. The traffic cop at the scene of the accident took careful measurements of the skid marks and the location of the vehicles (see diagram). The speed limit on both roads was 45 mph. Tracy told the policeman that she thought she was traveling between 40-45 mph when she first saw the white car cross in front of her. The policeman noted that Tracy's car (vehicle 2 on diagram) showed 20 feet of skid marks prior to impact while vehicle 1 showed no skid marks. After impact, both vehicles showed skid marks, with Tracy's car stopping at the curb, and the other car sliding an additional 5 feet on the grass. The traffic cop also noted that the roadway was mostly dry, while the grass was still damp from an earlier drizzle. The drag sled found the coefficient of friction of the roadbed to be 0.8. An ambulance came and took both drivers to the hospital - Tracy to the emergency room for an EKG, chest and neck x-rays and the driver of the other car to shock trauma

Explanation / Answer

given, Tracy : headed east

weight of car, M = 4300 lbs

weight of other car, m = 3100 lbs

length of skid marks by car 1 before impact, l = 20 ft

skid mnarks of both vehicles, d = 24.2 ft

skid marks of the car on the grass, c = 5 ft

coefficent of kinetic friction on the road, k = 0.8

1. let speed of car 1 ( tracy's car) before imact be u1

speed of other car be u2

speed after collision be v

then from the skidmarks

0.5*(m + M)v^2 = (m + M)*k*g*d

0.5v^2 = 0.8*32.2*24.2

v = 35.309 ft/s

From diagram approximate distance in east travelled by both cars is b = 22 ft

so angle of the skid maks with east direction, theta = arccos(22/24.2) = 24.619 deg

Now from conservation of momentum

Mu1 = (M + m)vcos(theta)

mu2 = (M + m)vsin(theta)

4300*u1 = 7400*35.309*cos(24.619)

u1 = 55.240 ft/s = 37.664 mph

similiarly

3100*u2 = 7400*35.309*sin(24.619) = 23.94 mph

2. initial speed of tracy = V

deceleration a = k*g = 0.8*32.2 = 25.76 ft/s/s

hence

2*a*l = V^2 - u1^2

2*25.76*20 = V^2 - 55.240^2

V = 63.889 ft/s = 43.45 mph

hence tracy was within tyhe speed limit

3. initial speed of the car 2 = V'

acceleration = 25.76 ft/s/s

final spoeed = u2 = 35.112 ft/s

distance travelled from red light to accident area = 33 - 11/2 = 27.5 ft

hence

2*25.76*27.5 = 35.112^2 - V'^2

V' cannot be +ve hence the other drived indeed started from rest

4. initial impact lasted t = 0.1 s

change in momentum of tracy = 115*[sqroot[(37.664 - 35.309*cos(24.619))^2 + (35.309*sin(24.619)^2)] = 1808.548 lbs ft/s

hence force = change in momentum / time = 18085.4879 lbs ft / s^2

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