The drawing shows two boxes resting on frictionless ramps. One box is relatively

Question

The drawing shows two boxes resting on frictionless ramps. One box is relatively light and sits on a steep ramp. The other box is heavier and rests on a ramp that is less steep. The boxes are released from rest at A and allowed to slide down the ramps. The two boxes have masses of 12 and 43 kg. If A and B are hA = 4.7 and hB = 1.7 m, respectively, above the ground, determine the speed of (a) the lighter box and (b) the heavier box when each reaches B. (c) What is the ratio of the kinetic energy of the heavier box to that of the lighter box at B?

I am posting this question because I could not "understand" other peoples work on this exact same question. Please be clear.

Explanation / Answer

a &b)

Height of the first box is h_A = 4.7 m
and h_B = 1.7 m
h_A - h_B = 4.7 m - 1.7 m = 3.0 m
speed of the lighter and heavier box are same
v = sqrt [2 * g * h] = sqrt [2 *9.8 *3.0]
v_A = v_B = 7.668 m/s
c )

ratio of k.E_lighter and K.E _heavier:
K.E_1 / K.E_2 = 1/2 m_A v_A^2 / 1/2 m_B v_B^2
= m_A / m_B
= 12 kg / 43 kg
= 0.279

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