If we recreated the scene from Fast & Furious 7 and dropped a Challenger SRT® Hellcat Redeye Widebody from a C-130 aircraft at 5,280 ft, how much horsepower would it take to drive past it before it hits the ground if you’re 1 mile away?
To calculate the horsepower required to drive past the falling car before it hits the ground, we need to determine the time it takes for the car to reach the ground after being dropped from the aircraft. Then, considering the distance you need to cover in one mile, we can calculate the speed required and convert it into horsepower.
Step 1: Calculate the time it takes for the car to fall from 5,280 ft:
Using the formula for time of fall, t = √(2h/g), where h is the initial height and g is the acceleration due to gravity (approximated as 32.2 ft/s²).
t = √(2 * 5280 / 32.2)
t ≈ √(3280 / 16.1)
t ≈ √203.7
t ≈ 14.27 seconds (rounded to the nearest hundredth)
Step 2: Calculate the required speed to cover one mile in 14.27 seconds:
One mile is equal to 5,280 feet.
Required speed = Distance / Time
Required speed = 5,280 ft / 14.27 s
Required speed ≈ 369.43 ft/s
Step 3: Convert the speed to miles per hour:
1 mile = 5,280 feet
1 hour = 3,600 seconds
Required speed (mph) = Required speed (ft/s) * 0.681818 (conversion factor)
Required speed (mph) ≈ 369.43 ft/s * 0.681818
Required speed (mph) ≈ 252.03 mph (rounded to the nearest hundredth)
Step 4: Calculate the horsepower required to achieve the necessary speed using the power equation: horsepower = (force * velocity) / 550.
Assuming a mass of the car m ≈ 4,492 lbs (the weight of a Challenger SRT® Hellcat Redeye Widebody), and considering the gravitational force F = m * g, where g is approximately 32.2 ft/s², we can calculate the force.
Force = 4492 lbs * 32.2 ft/s²
Force ≈ 144,740 lb·ft/s²
Convert lb·ft/s² to horsepower:
1 horsepower (HP) = 550 lb·ft/s²
Horsepower = (Force * velocity) / 550
Horsepower ≈ (144,740 lb·ft/s² * 252.03 mph) / 550
Horsepower ≈ 66,309.52 HP (rounded to the nearest hundredth)
Therefore, to drive past the falling car from a distance of 1 mile before it hits the ground, it would take approximately 66,309.52 horsepower.