Answer: The final speed of the incoming ball is approximately 200m/s
Step-by-step explanation:
Using the law of conservation of momentum.
m1(u1) + m2u2 = m1v1 + m2v2
And also law of conservation of kinetic energy for elastic heads on collision we can derive the formula for elastic heads on collision which is given below:
For elastic heads on collision.
v1 = [( m1 - m2)/(m1+m2)] u1 ......1
v2 = [(2m1)/(m1+m2)]u1 ......2
Where,
m1 and m2 are the mass of the incoming and stationary ball respectively.
u1 and u2 are the initial speed of the incoming and stationary ball respectively.
v1 and v2 are the final speed of the incoming and stationary ball respectively.
a) to determine the final speed of the incoming ball using equation 1
v1 = [( m1 - m2)/(m1+m2)]u1
Since m1 >> m2
m1 - m2 ~= m1 and m1 +m2 ~= m1
So, equation 1 becomes
v1 ~= [m1/m1]u1
v1 ~= u1
Since u1 = 200m/s
v1 ~= 200m/s
Additional tips: using equation 2 we can derive the approximate final speed of the stationary ball following the same assumptions. If well solved v2 = 2u1 = 400m/s