8)Answer: 20.362 m/s
Step-by-step explanation:
According to the law of conservation of momentum,
Total momentum before collision = total momentum after collision
Total momentum before collision = m1u1 + m2u2
where
m1 is the mass of the object moving to the right
u1 is its velocity
m2 is the mass of the object at rest
u2 is its velocity
From the information given,
m1 = 13
u1 = 26
m2 = 10
u2 = 0
Total momentum before collision = 13 x 26 + 10 x 0 = 338
Total momentum after collision = m1v1cosθ1 + m2v2cosθ2
where
θ1 is the angle made by m1 with the horizontal
θ2 is the angle made by m2 with the horizontal
v1 is the final velocity of m1 after collision
v2 is the final velocity of m2 after collision
From the information given,
v1 = 11
θ1 = 20
Total momentum = 13 x 11cos20 + 10v2cosθ2 = 134.376 + 10v2cosθ2
Thus,
338 = 134.376 + 10v2cosθ2
10v2cosθ2 = 338 - 134.376 = 203.624
v2cosθ2 = 203.624/10
v2cosθ2 = 20.362 m/s
The x component of the velocity of the 10kg ball after collision is 20.362 m/s