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I was curious of the athleticism I'd need to dunk a standard rim at $10$ ft above the ground. Using an online calculator, given that I am $5$ feet $6$ inches tall with a standing reach of $7$ feet $1$ inches, I apparently have to have a vertical jump of $35$ inches to at least touch the rim and $41$ inches to dunk because of the space between my fingertips and the rim while carrying the ball, which all seems reasonable.

Given my weight of $190$ pounds the calculator also said I must have a takeoff speed of $4.52$ meters per second with a force $6515$ Newtons assuming I make my leap bending my knees at a $60$ degree angle.

I understand that $$\underbrace{10 \ \text{ft}}_{\text{rim height}} - \underbrace{7.08 \ \text{ft}}_{\text{standing reach}}=2.92 \ \text{ft} \equiv {35.04 \ \text{in}\ }+6 \ \text{in gap} \implies \underbrace{41.04 \ \text{inches}}_{\text{required vertical jump to dunk}}$$ This checks out. But I'm suspicious of the other results, so how do I come to confirming them? Or how do I get much more tangibly accurate numbers myself?

Using $F=MA$ I get $\approx 8291 \ N$, so I'm guessing this equation doesn't cover all bases needed for force. I'd also like to consider the downward acceleration prior to the jump and of course the energy to reach our desired height $h$. I'm just not sure how to incorporate all of this. Can anyone help out?

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  • $\begingroup$ Well, projectile motion is independent of the mass, so not sure why your answer depends on mass. If you want to consider the force, it's a little trickier because you need to account for the time over which you apply the force. What you could try to calculate is the work done or change in momentum to gain the necessary liftoff velocity, then estimate how long your foot is pushing during liftoff, and estimate the average force needed. $\endgroup$ – Feel My Black Hole Aug 6 at 6:56

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