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If the change in energy (ΔE) is expressed in joules and the change in time (Δt) in seconds, the power is indicated in watts. Since we already know the change in energy (42 thousand joules), we are left with only da calculate the time it takes Batman to travel the ten floors.
As is often the case in cinema, there are cuts in the film between different shots and angle variations, which mean that the timing is not entirely clear. Approximating, however, I would say that Batman employed 6 seconds to go from the ground floor to the tenth. This means that the power required by the battery is 7,164 watts.
We are talking in a considerable amount of energy. If we wanted to compare it to that needed to power a car, we would have to convert the value into horsepower, and we would get a rather low figure: ten horsepower. Most cars have at least 150 horsepower engines.
However, this data is not bad when it comes to a person. According to experimental data from NASA, a human in excellent shape can produce about 800-1000 watts of power for 6 seconds. But not 7000 watts. It’s not possible, even if the person in question is Batman.
Then there is another problem with the gun and its battery. While an iPhone’s battery may have enough power to power the grapple shooter for a 10-story climb, it would not be enough to make the escape in 6 seconds. Suppose we have a 3.8 volt battery with a power of 7000 watts. We would need an electrical current of over 1800 amps. We are talking about a very high value, which would heat (or melt) the cables that go from the motor to the gun, requiring even more power. greater.
A normal iPhone battery wouldn’t be enough. One would be needed much larger battery and with a higher voltage in order to reduce the current. But bigger batteries are heavier, and that would mean that a bigger gun would be needed.
For the avoidance of doubt: it is possible to make a grappling gun, as you can see in the video below, which shows a seemingly working DIY example. Such a device probably comes closest to what it would take to hoist a human through several flights of stairs. The version built in the video however is bulkier and slower than the Batman gadget. The gun in the video uses batteries that can fit in trouser pockets, but it also has much larger electric motors.
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