Question

a 4.0 kg firecracker originally at rest explodes into two pieces. the 1.5 - kg chunk moves left at 10 m/s. calculate how fast the 2.5 - kg chunk moves to the right.
a 6 m/s
b 10 m/s
c 17 m/s
d 26 m/s

Explanation:

Step1: Apply conservation of momentum

The initial momentum of the fire - cracker is $P_i = 0$ (since it is at rest, $v_i=0$ and $P = mv$). Let the mass of the first piece $m_1 = 1.5$ kg, its velocity $v_1=- 10$ m/s (negative because it moves to the left), and the mass of the second piece $m_2=4.0 - 1.5=2.5$ kg, and its velocity be $v_2$. According to the law of conservation of momentum $P_i = P_f$, so $0=m_1v_1 + m_2v_2$.

Step2: Solve for $v_2$

We can re - arrange the equation $0=m_1v_1 + m_2v_2$ to get $v_2=-\frac{m_1v_1}{m_2}$. Substitute $m_1 = 1.5$ kg, $v_1=-10$ m/s, and $m_2 = 2.5$ kg into the formula. Then $v_2=-\frac{1.5\times(- 10)}{2.5}=\frac{15}{2.5}=6$ m/s.

Answer:

A. 6 m/s