We may further assume that, to get the impulse, he pushes down with the entire area of his foot to get a vertical boost. We can approximate the protagonist’s foot as a rectangle with size a total surface area A of 200 cm 2 for the foot. Inserting the numbers in the equation above, we conclude that the force F on him from the crane is 11,800 Newtons. Overall, accepting the value Δ t=0.1 s for our hero is a reasonable assumption. This duration does depend on technique too. For high and long jumpers this time increases slightly since the athlete has to press down on the ground Such an interaction always lasts a fraction of a second įor sprinters this is about 0.1 s. Data from athletes show that the faster the movement of the sport, the shorter the contact time Δ t with the ground. Know how long the action-reaction between him and the crane lasted. Hence, we can compute the force F on him from this equation, J = F Δ t which, in turn, produces the (change of) momentum m v 0 y:Īccording to Wikipedia, Dwayne Johnson’s mass is 118 kg. The crane reacts: it applies the vertical (exactly opposite) force F during the same time interval, thus producing the impulse Athletes utilize impulses from the ground to thrust themselves high in almost all sports.Īt the edge of the crane, the protagonist pushes with his foot down on the crane for a brief interval Δ t. Achieving it along the vertical direction however is not a matter of running it is achieved by an impulse from the crane along the vertical direction. Achieving this speed along the horizontal direction is solely an issue of human performance it can only be achieved by running. Have we then reached a final conclusion that the feat is not possible? Not yet. Then, from equation ( 3), we conclude that v 0 y is of the orderġ0 m/s. In fact, from the trailer we clearly see that this is what the director has in his mind.Īgain from the trailer, we can see that the peak point of the trajectory is achieved approximatelyĪbout a second after the jump. Having decided that it is impossible to do the jump with zero initial vertical speed, let’s now explore the possibility to perform the feat with a non-vanishing vertical speed. In fact, since the protagonist is an extended object and not a point, we may assume that point C is the highest possible point which he should reach in order to be able to pass through the window. That L ∼ 10 ℓ (it appears to be more), h ∼ 5 ℓ (it appears to be less than half of L), w ∼ 2 ℓ (it appears to be less a 3-meters window appears to be a decent assumption). The reader can also easily check with the use of a ruler Since the legs of the protagonist are not fully extended, we will assume that ℓ ≃1.5 meters. In doing so, since the action is shown through a viewing angle that favors visual pleasureīut it is not optimal for the collection of data, we will approximate the various quantities in favor of the director to avoid any criticism for unfairness. Size of the window w, the distance L between the crane and the skyscraper, and the vertical distance h from the bottom of the In particular, one can compare the size ℓ of the protagonist with the The difference from a standard problem is that the student will have to decide what is known by relying on the visual information provided by the director in the film.
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