Answer:
a) p₃ = 5 kg*m/s
b) v₃ = 33.33 m/s
Explanation:
Given
m₁ = 0.200 kg
v₁ = 20.0 m/s i
m₂ = 0.100 kg
v₂ = 30.0 m/s j
m₃ = 0.150 kg
a) Using the equation p = m*v
p₃ = ?
If p₁ = m₁*v₁
and
p₂ = m₂*v₂
v = 0 m/s (speed of the the Physics textbook before the explosion)
m = mass of the Physics textbook before the explosion
We apply the following Principle
m*v = p₁ + p₂ + p₃
then
m*0 = m₁*v₁ + m₂*v₂ + p₃
⇒ 0 = (0.200 kg)*(20.0 m/s i) + (0.100 kg)*(30.0 m/s j) + p₃
⇒ 0 = 4 kg*m/s i + 3 kg*m/s j + p₃
⇒ p₃ = - 4 kg*m/s i - 3 kg*m/s j (i)
and its module is
[tex]p_{3} =\sqrt{(-4)^{2} +(-3)^{2} } kg*\frac{m}{s} = 5 kg*\frac{m}{s}[/tex]
b) Using equation (i):
p₃ = - 4 kg*m/s i - 3 kg*m/s j
⇒ m₃*v₃ = - 4 kg*m/s i - 3 kg*m/s j
⇒ (0.150 kg)*v₃ = - 4 kg*m/s i - 3 kg*m/s j
⇒ v₃ = (- 4 kg*m/s/(0.150 kg)) i - (3 kg*m/s/(0.150 kg)) j
⇒ v₃ = - 26.67 m/s i - 20 m/s j
and its module is
[tex]v_{3} =\sqrt{(- 26.67)^{2} +(- 20)^{2} } \frac{m}{s} = 33.33 \frac{m}{s}[/tex]
