Answer :
We need to use the formula: Force = Mass × Acceleration Let's use the given values to calculate the force exerted on the deer when it is hit by the car. The car weighs 235 lb and it is traveling north at 75 mph. The deer weighs 150 lb and it is going 35 mph east. Force = 44045 lbSince the force is a vector quantity, it has both magnitude and direction.
Step 1: Convert the velocities into feet per second.1 mile = 5280 feet1 hour = 3600 seconds So, the velocity of the car is:75 mph = (75 × 5280) ÷ 3600 = 110 feet/secondThe velocity of the deer is:35 mph = (35 × 5280) ÷ 3600 = 51.3 feet/second
Step 2: Find the components of velocity of the deer. The velocity of the deer is in the east direction, so we need to find its horizontal component, vx, and its vertical component, vy. If the angle between the deer's velocity and the x-axis is θ, then: vx = v × cosθandvy = v × sinθv = 51.3 feet/secondθ = 90° - arctan(0 / 110) = 90°So,vx = 51.3 × cos90° = 0 feet/second vy = 51.3 × sin90° = 51.3 feet/second
Step 3: Find the net velocities of the car and the deer. Since the car is moving north and the deer is moving east, the net velocity of the car and deer together can be found using the Pythagorean theorem. Net velocity = √[(vx + 110)² + vy²]Net velocity = √[(0 + 110)² + (51.3)²]Net velocity = √(12100 + 2631.69)Net velocity = √14731.69Net velocity = 121.3 feet/second
Step 4: Find the net momentum of the car and the deer. Net momentum = (mass of car × velocity of car) + (mass of deer × velocity of deer)Net momentum = (235 × 110) + (150 × 121.3)Net momentum = 25850 + 18195Net momentum = 44045 lb ft/second
Step 5: Find the force exerted on the deer. Force = Net momentum ÷ time Here, time is the duration of the collision which is not given in the problem. We will assume it to be 1 second. Force = 44045 ÷ 1
Force = 44045 lb Since the force is a vector quantity, it has both magnitude and direction. The direction of force is along the line of impact which is not given in the problem.
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