Answer:
the person will be in the shore at 10.73 minutes after launch the shoe.
Explanation:
For this we will use the law of the lineal momentum.
![L_i = L_f](https://tex.z-dn.net/?f=L_i%20%3D%20L_f)
Also,
L = MV
where M is de mass and V the velocity.
replacing,
![M_i V_i = M_{fp}V_{fp} + M_{fz}V_{fz}](https://tex.z-dn.net/?f=M_i%20V_i%20%3D%20M_%7Bfp%7DV_%7Bfp%7D%20%2B%20M_%7Bfz%7DV_%7Bfz%7D)
wher Mi y Vi are the initial mass and velocity, Mfp y Vfp are the final mass and velocity of the person and Mfz y Vfz are the final mass and velocity of the shoe.
so, we will take the direction where be launched the shoe as negative. then:
(70)(0) = (70-0.175)(
) + (0.175)(-3.2m/s)
solving for
,
= ![\frac{(3.2)(0.175)}{69.825}](https://tex.z-dn.net/?f=%5Cfrac%7B%283.2%29%280.175%29%7D%7B69.825%7D)
= 0.008m/s
for know when the person will be in the shore we will use the rule of three as:
1 second -------------- 0.008m
t seconds-------------- 5.15m
solving for t,
t = 5.15m/0.008m
t = 643.75 seconds = 10.73 minutes