Question 1 (25 points) Mike the Georgia State Patrolman is the first to respond to a vehicle accident where a driver hit a deer. After making sure no one is seriously injured, he assesses the situation. If the skid marks are 76 feet long and Mike assumes the drag factor is 0.8, what is the minimum speed Mike knows the driver was going when he hit the brakes? a) 42.7 mph b) 32.8 mph c) 46.4 mph d) 37.9 mph

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Question 1 (25 points) Mike the Georgia State Patrolman is the first to respond to a vehicle accident where a driver hit a deer. After making sure no one is seriously injured, he assesses the situation. If the skid marks are 76 feet long and Mike assumes the drag factor is 0.8, what is the minimum speed Mike knows the driver was going when he hit the brakes? a) 42.7 mph b) 32.8 mph c) 46.4 mph d) 37.9 mph

Answer 1

The minimum speed the driver could have been going is \(42.7 \mathrm{mph}\).

Answer 2

## Step 1 The formula to determine the speed of a vehicle based on skid marks is given by: ### \(v = \sqrt{2 \times f \times g \times d}\) Where: \(v\) = speed of the vehicle (in feet per second) \(f\) = drag factor (given as 0.8) \(g\) = acceleration due to gravity (approximately 32.2 ft/s\(^2\)) \(d\) = skid mark length (given as 76 feet) ## Step 2 Plugging in the given values: ### \(v = \sqrt{2 \times 0.8 \times 32.2 \times 76}\) ## Step 3 Calculating the above expression gives the speed in feet per second. First, compute the value inside the square root: ### \(2 \times 0.8 \times 32.2 \times 76 = 3911.68\) Then, ### \(v = \sqrt{3911.68} \approx 62.55\) feet per second ## Step 4 To convert this to miles per hour (mph), multiply by a factor of \(\frac{3600}{5280}\): ### \(v_{\text{mph}} = 62.55 \times \frac{3600}{5280} \approx 42.7\) mph ## Step 5 The calculated speed is approximately 42.7 mph, which corresponds to option a).

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