A 86kg person jumps and plunges 2.6m deep into water before coming to a stop. How can I find the force of friction from the water?

Question

Their velocity before hitting the water is $10.48m/s$, and I want to use the conservation of energy formulas. I also went ahead and calculated the acceleration $(13.62m/s^2)$(edit: its $21.12m/s^2$), in hopes that would help, by using $F=ma$, but that's not how you calculate friction, haha...

I'm a high school student in Physics 11, and amidst this pandemic, it is very difficult to understand our new unit, so it's very frustrating that I'm not doing so well on the practice. Any and all help is appreciated! I just wish to better understand this unit before school is over.

Answer 1

There are two equivalent ways. One, calculate the acceleration using $v_f=0$:$$v_f^2=v_i^2+2ad$$so $$a=\frac{v_i^2}{2d}$$ Then the force acting on the body is $F=ma$. But note that $F$ is the sum of the forces. Gravity is acting downwards and friction is up. So $$F_f-mg=ma=m\frac{v_i^2}{2d}$$ The equivalent way to get the formula you get from energy. If you would multiply the above by $d$ and rearranging terms, you get $$F_f d=\frac{mv_i^2}2+mgd$$ The meaning of this is to say that the initial energy (kinetic+potential) is equivalent to the work done by friction

Answer 2

A body immersed in the water remains floating (more or less up to the kin) because of buoyancy: the famous eureka of Archimedes ! Buoyancy (almost) compensates for gravity.

So, when immersed, you can assume that the potential energy of gravitation+ buoyancy is almost null.

So the kinetic energy at entering the water will be mainly dissipated by friction. The friction force depends very much on the speed, however its average value will be such as to do a work equal to $F_f \cdot 2.6$ Joule, which shall null the kinetic energy of $1/2*86*(10.48)^2$, i.e. $F_f = 1816 N$ or about 182 kg.