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since the block slide down at a constant speed, all forces are balance.
the force that causes the block to slide down is
sin(36.4)mg, which is equal to the friction force
friction = ? cos(36.4)mg
?cos(36.4)mg = sin(36.4)mg
?cos(36.4) = sin(36.4)
? = 0.737
final energy = initial energy - work done by friction
the final energy of the block is the potential energy
initial Energy is the kinetic energy
work done by friction = ?cos(36.4)mg sin(36.4)/h
mgh = .5mv² - ?cos(36.4)mg sin(36.4)/h
gh = .5v² - 0.737 cos(36.4)g sin(36.4)/h
9.8h = .5(2.6)² - 0.737 cos(36.4)(9.8) h/sin(36.4)
9.8h = 3.38 - 9.79h
19.59h = 3.38
h = 0.172m [this is the altitude]
sin(36.4) = h/L
L = .172 / sin(36.4)
L = 0.29m <== answer
hope it helps :-)
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