Two people are standing on a 1.75-m-long platform, one at each end. The platform floats parallel to the ground on a cushion of air, like a hovercraft. The two people, the platform and a 5.76-kg ball are all initially at rest. One person throws the 5.76-kg ball to the other, who catches it. The ball travels nearly horizontally. Excluding the ball, the total mass of the platform and people is 184 kg. Because of the throw, this 184-kg mass recoils. How far does the platform move before coming to rest again?

0.05312 m

Explanation:

Given:

Length of platform L = 1.75 m

mass of ball m_b = 5.76 kg

mass of (people + platform) m_p = 184 kg

Initial Velocity of ball V_i, b = 0

Initial Velocity of ball (people + platform) V_i, p = 0

Find:

How far does the platform recoils to rest

Solution:

Using the conservation of momentum on ust before and after the ball was thrown P_i = P_f:

Where, P_i = 0 (initially at rest)

P_f = m_p*V_f, p + m_b * V_f, b

0 = m_p*V_f, p + m_b * V_f, b

V_f, p = - (m_b / m_p) * V_f, b

V_f, p = - (5.76 / 184) * V_f, b

V_f, p = - 0.0313*V_f, b ... 1

The time the ball is in air:

t = L / (V_f, b - V_f, p) ... 2

The distance that the platform moves d:

d = V_f, p * t ... 3

Substitute 2 into 3

d = V_f, p*L / (V_f, b - V_f, p) ... 4

Solve 1 and 4 simultaneously:

d = - m_b*L / (m_b + m_p)

d = - 5.76*1.75 / (5.76 + 184)

d = - 0.05312 m

The platform moves 0.05312 m to the opposite to which the ball is thrown.