Answer:
vf₂ = 15.79 m/s
Explanation:
Theory of collisions
Linear momentum is a vector magnitude (same direction of the velocity) and its magnitude is calculated like this:
p=m*v
where
p:Linear momentum
m: mass
v:velocity
There are 3 cases of collisions : elastic, inelastic and plastic.
For the three cases the total linear momentum quantity is conserved:
P₀ = Pf Formula (1)
P₀ :Initial linear momentum quantity
Pf : Final linear momentum quantity
Data
m₁ = 2600 kg : mass of the rhino
m₂= 0.18 kg : mass of the ball
v₀₁ = 3.70 m/s : initial velocity of the rhino
v₀₂= - 8.39 m/s, initial velocity of the ball
Problem development
We appy the formula (1):
P₀ = Pf
m₁*v₀₁ + m₂*v₀₂ = m₁*vf₁ + m₂*vf₂
(2600)*(3.7) + (0.18)*(- 8.39) = (2600)*vf₁ +(0.18)*vf₂
9620 -1.5102 = (2600)*vf₁ +(0.18)*vf₂
9618.4898 = (2600)*vf₁ +(0.18)*vf₂ Equation (1)
Because the shock is elastic, the coefficient of elastic restitution (e) is equal to 1.
[tex]e = \frac{v_{f2}-v_{f1} }{v_{o1}-v_{o2}}[/tex]
1*( v₀₁- v₀₂ ) = (vf₂ -vf₁)
( 3.7 -( -8.39 ) = (vf₂ -vf₁)
12.09 = (vf₂ -vf₁)
vf₂ = vf₁ + 12.09 Equation (2)
We replace Equation (2) in the Equation (1)
9618.4898 = (2600)*vf₁ +(0.18)*vf₂
9618.4898 = (2600)*vf₁ +(0.18)* (vf₁ + 12.09)
9618.4898 = (2600)*vf₁ +(0.18)*vf₁ + (0.18)(12.09)
9618.4898 = (2600)*vf₁ +(0.18)*vf₁ + 2.1762
9618.4898 -2.1762 = (2600.18)*vf₁
9616.3136 = (2600.18)*vf₁
vf₁ = (9616.3136) / (2600.18)
vf₁ = 3.698 m/s : Final velocity of the rhino
We replace vf₁ = 3.698 m/s in the Equation (2)
vf₂ = vf₁ + 12.09
vf₂ = 3.698 + 12.09
vf₂ = 15.79 m/s : Final velocity of the ball
