how long would it take a lexus to fall 4000 feet, and what would be the velocity?

Question

I just saw a Lexus commercial. It had (simulated, of course) one Lexus dropped from a helicopeter from 4000 feet. It had another one on the ground, which started from a dead stop 4000 feet from where the dropped Lexus would hit. The driven car passed underneath the dropped vehicle before the dropped one hit the ground. So, in theory, the driven car was moving faster than the dropped one. Unfortunately, my math skills aren't up to figuring out how fast either car was moving, and how long it took them to get up to that speed. Any one with an answer? And thanks in advance.

Answer 1

Distance traveled under constant acceleration
s=.5gt^2

t=sqrt(2s/g)
g=32 ft/s^2 then
t=sqrt(2 x 4000/32)
t=15.81sec

Velocity under constant acceleration is
V=at

or V=gt in this case

V=32 x 15.81sec=505 ft/sec
V=344 m/h

Even considering the air braking the commercial is pushing the limits of reality.

Answer 2

Hey,
I was just thinking about that comercial as well. Here are my thoughts:

Some cars have top speeds that are electronically limited (as is the case with my Jetta), where the computer tells the car what the maximum speed can be. Other cars are "drag limited," which, per my understanding, means that they can't exceed a particular speed because of aerodynamic factors (aerodynamic interference at a particular speed creates more force than the engine is able to exert at that speed). It seems to me that this must be close to the car's terminal velocity, assuming that the car were falling nose first. The car in the commercial is falling wheels first, which would create considerably greater aerodynamic interference than if the car were falling nose first. Thus, it is conceivable that if the car actually fell 4000 feet (.76 miles) wheels first, then the car on the ground might be able to exceed the speed of the falling car, thereby "catching up" to the falling car.

I don't know what the 1/4 mile time/speed of the Lexus is, but let's guess that it's around 90 mph. The terminal velocity for a falling human body (ie skydiver) is around 135 mph. Because a human body is considerably more sleek than is a car that is falling wheels first, I am going to make a while guess that the speed of the falling Lexus couldn't be in excess of this figure.

Without actually running the numbers, I'm going to guess that this is feasible, but I don't have any figures to back that up.

I need to get out more.

Answer 3

How heavy was the Lexus? Gravity pulls on everything at 10 meters per second per second. Without knowing the weight of the Lexus let alone the time it took to reach the ground, it would be incredibly difficult to calculate the velocity of the Lexus as it fell to its death.

Answer 4

You don't need to do any math to realize no crappy toyota engine is going to beat 1 g acceleration.