A ball with a mass of 6 kg is rolling at 25 m/s and elastically collides with a resting ball with a mass of 1 kg. What are the post-collision velocities of the balls?

1 Answer
Apr 12, 2016

v_1^'=125/7 m/s
v_2^'=300/7 m/s

Explanation:

vec P_1+vec P_2:" total momentum before collision "
vec P_1^'+vec P_2^':" total momentum after collision"
vec P_1+vec P_2=vec P_1^'+vec P_2^'" conservation of momentum"

m_1*v_1+m_2*v_2=m_1*v_1^'+m_2*v_2^'
6*25+1*0=6*v_1^'+1*v_2^'
150=6*v_1^'+1*v_2^'" (1)"

v_1+v_1^'=v_2+v_2^'" (2)"
25+v_1^'=0+v_2^'
v_2^'=25+v_1^'" (3)"

"let's use (1)"
150=6*v_1^'+25+v_1^'
150-25=7v_1^'
125=7v_1^'
v_1^'=125/7 m/s

"let's use (3)"
v_2^'=25+125/7
v_2^'=(175+125)/7
v_2^'=300/7 m/s