Question

1. little ms. hernandez recoils backward at 2.0 m/s after firing a projectile at 120 m/s. little ms. hernandez has a mass of 30 kg. what is the mass of the projectile?
2. little mr. reed has a mass of 22 kg. he recoils backward at 1.1 m/s after firing a dart with mass 0.25 kg. what is the dart’s speed?

Explanation:

Step1: Apply conservation of momentum

Initial total momentum = 0, so $m_1v_1 + m_2v_2 = 0$, rearranged to $m_2 = -\frac{m_1v_1}{v_2}$ (negative sign accounts for opposite direction, we use magnitudes for mass)

For question 5:

$m_1 = 30\ \text{kg}$, $v_1 = -2.0\ \text{m/s}$, $v_2 = 120\ \text{m/s}$
$m_2 = -\frac{30 \times (-2.0)}{120}$

Step2: Calculate projectile mass

$m_2 = \frac{60}{120} = 0.5\ \text{kg}$

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Step1: Apply conservation of momentum

Use $m_1v_1 + m_2v_2 = 0$, rearranged to $v_2 = -\frac{m_1v_1}{m_2}$

For question 6:

$m_1 = 22\ \text{kg}$, $v_1 = -1.1\ \text{m/s}$, $m_2 = 0.25\ \text{kg}$
$v_2 = -\frac{22 \times (-1.1)}{0.25}$

Step2: Calculate dart speed

$v_2 = \frac{24.2}{0.25} = 96.8\ \text{m/s}$

Answer:

1. The mass of the projectile is $\boldsymbol{0.5\ \text{kg}}$
2. The dart's speed is $\boldsymbol{96.8\ \text{m/s}}$