Speed

BBC

Speed was the 1994 smash hit film starring Keanu Reeves and Sandra Bullock. Keanu Reeves plays Jack Traven, an LAPD SWAT team specialist who is sent to defuse a bomb that a revenge-driven extortionist (Dennis Hopper) has planted on a crowded bus. Bullock has to maintain the velocity of the bus at 50mph (or greater) so that the bomb does not explode, killing all on board.

The film is a high-octane race of suspense, non-stop action and surprise twists. In a heart stopping, adrenalin pumping moment, the bus turns onto an uncompleted section of a freeway overpass, with a 50-foot gap in the road. Of course they leap the gap - this is Hollywood!

Our Hollywood Scientists, using their unique backyard technology, prove the flaws in the movie’s thesis. But what forces are at work in Speed, and how fast and at what angle does the bus have to be to make it? How could you work this out theoretically?

We decided to find out...

If you watch the film, the section of the freeway they are jumping appears to be flat. It does not look like there is any kind of ramp, an angled surface, to jump off. This is a problem. Why? Because vertical motion and horizontal motion are independent of each other. What does this mean? Let’s look at each one in turn.

Vertical Motion: objects falling due to gravity, or aeroplanes rising, overcoming gravity.

If we consider an object falling due to gravity, how long would it take to fall a set distance?

If an object falls from rest, then it will fall at approximately 10 ms^-2, due to the constant pull of the earths gravity.

So how fast will it be falling after 5 seconds?

If speed = acceleration x time then

10 x 5 = 50 ms^-1 or 180km/hr.

That is the final vertical speed, but what would the average speed have been? If you are accelerating at a constant rate (and when falling you usually are) then the average speed would be half of the final speed so it will be 25 ms^-1 So how far would the object have fallen in 5 seconds? 25 x 5 = 125 metres.

Here come the equations!

This can be written as:
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So now we want to do two calculations, firstly, the time it takes to jump a 50ft hole in the freeway, and secondly how far the bus will fall in this time.

If the bus is travelling above 50mph, (let’s give them the benefit of the doubt and assume it is going about 75mph (33ms^-1)).

To travel 50ft (15.24m which is 3.28ft to a metre), will take

15.24/33.5 = 0.454 seconds.

In that time the bus will have fallen - according to our formula s=0.5at²:

0.5 x 10 x 0.454² = 1.03m

So does the film hold up scientifically?

BBC Nope!

If the bus took off from a flat surface and tried to land on another flat surface the same height, as it appears to in the film, it would not have been possible. The bus would have fallen 2.27m and crashed into the raised freeway. Nasty!

Bus with no ramp:

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To clear the 50ft gap on the freeway, what is needed is a jump (an angled surface) So why is this and what angle is required? If we take an angle of, say, 30 degrees, then travelling at 75mph the bus will start with an initial upwards velocity (speed in certain direction). What would the upwards (vertical) and horizontal velocities be?

Bus with ramp:

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If the bus is taking off (literally) at a 30 degree angle, at 75mph, then there will be a motion upwards (vertical) and a motion forwards (horizontal). These motions are independent of each other, which means you can split them up and work out how far the bus travels, upwards/downwards and forwards/backwards.

This is done using good old trigonometry.
So for the vertical motion the speed at which the bus is going upwards initially is:

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The bus would decrease in speed upwards due to gravity, until it stops and then start falling, like throwing a ball upwards. How long would the bus take to rise and fall to the same level?

Final speed = initial speed + (acceleration x time)

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1.675 seconds to reach the top of its flight.

How high has the bus gone, before it starts to comes down?

Average speed = (initial speed + final speed)/2 for a constant acceleration.

Therefore:

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The height climbed in 1.675 seconds is then:

8.375 x 1.675 =14m.

To fall 14m due to gravity will take how long? Another 1.67 seconds. So the total time will be approximately 3.3 seconds.

That’s how long you have to make the jump, but is this enough? Can the bus move forwards 50ft in 3.3 seconds? What is the horizontal velocity?

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Therefore in 3.3 seconds the bus would travel

29 x 3.3 = 95.7m (314ft).

No problem: the bus would fly over the hole. We can see the effect of the angle on time and length of jump in this table.

We haven’t accounted for deceleration due to wind resistance, which is a variable, and could greatly reduce the distance jumped.

Next time you are racing along in a bus trying to prevent a bomb blowing up, take your eyes off Keanu Reeves/Sandra Bullock. If you want to know if you can scale that gap in the road, get out your calculator!

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