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After skiding down a snow-covered hill on an inner tube, Ashley is coasting across a level snowfield at a constant velocity of +2.6 m/s. Miranda runs after her at a velocity of +5.1 m/s and hops on the inner tube. How fast do the two of them slide across the snow together on the inner tube? Ashley's mass is 56 kg, and Miranda's is 64 kg. Ignore the mass of the inner tube and any friction between the inner tube and the snow.

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Answer:

3.93 m/s

Explanation:

[tex]m_1[/tex] = Mass of Ashley = 56 kg

[tex]m_2[/tex] = Mass of Miranda = 64 kg

[tex]u_1[/tex] = Initial Velocity of Ashley = 2.6 m/s

[tex]u_2[/tex] = Initial Velocity of Miranda = 5.1 m/s

v = Velocity of combined mass

As linear momentum is conserved

[tex]m_1u_1 + m_2u_2 =(m_1 + m_2)v_c\\\Rightarrow v_c=\frac{m_1u_1 + m_2u_2}{m_1 + m_2}\\\Rightarrow v=\frac{56\times 2.6 + 64\times 5.1}{56 + 64}\\\Rightarrow v=3.93\ m/s[/tex]

The speed at which they both slide down together is 3.93 m/s

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