A 20.00kg lead sphere is hanging from a hook by a thin wire 3.50m long and is free to swing in a complete circle. Suddenly it is struck horizontally by a 5.00kg steel dart that embeds itself in the lead spehere, what must the minimum initial speed of the dart so that the combination makes a complete circular loop after the collision.
I dont know what I'm doing wrong, this stuff isnt that hard but for some reason I'm getting the wrong answer.
p_1 = p_2
m_a * v_a1 + m_b + v_b1 = v_f(m_a + m_b)
v_b1 = v_f(m_a + m_b)/m_b
v_f must be great enough for the system to have enough energy to rise 7.0m.
1/2(m_a + m_b)v_f^2 = (m_a + m_b)gh
v_f = sqrt(2gh) -> v_f = sqrt(2 * 9.8m/s/s * 7.0m) = 11.713m/s
v_b1 = v_f(m_a + m_b)/m_b = (11.713m/s)(25kg)/5kg = 58.565m/s
However, the book is saying the answer is 65.5 m/s, what am I doing wrong?