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A student stumbles backward off a dock and lands in a small boat. The student isn’t hurt, but the boat drifts away from the dock with a velocity of 0.85 m/s to the west. If the boat and student each have a mass of 68 kg, what is the student’s initial horizontal velocity

Respuesta :

skyluke89

The initial velocity of the student is 1.7 m/s

Explanation:

We can solve this problem by using the law of conservation of momentum: in fact, the total momentum of the student-boat system must be conserved in absence of external forces, therefore we can write:

[tex]p_i = p_f\\mu = (m+M)v[/tex]

where:

m = 68 kg is the mass of the student

u is the initial velocity of the student

M = 68 kg is the mass of the boat

v = 0.85 m/s is their final combined velocity

Solving for u, we find the initial velocity of the student:

[tex]u=\frac{m+M}{m}v=\frac{68+68}{68}(0.85)=1.7 m/s[/tex]

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