Question

a frog is sitting on a lily pad when it sees a delicious fly. he darts out his tongue at a speed of 6.50 m/s to catch the fly. the tongue has a mass of 0.410 g, and the rest of the frog plus the lily pad have a mass of 13.0 g. what is the recoil speed of the frog and the lily pad? ignore drag forces on the pad due to the water.

Explanation:

Step1: Apply Conservation of Momentum

The total initial momentum is \(0\) (system at rest). Let \(m_1 = 0.410\,\text{g}\), \(v_1 = 6.50\,\text{m/s}\), \(m_2 = 13.0\,\text{g}\), and \(v_2\) be the recoil speed. By conservation of momentum: \(m_1v_1 + m_2v_2 = 0\).

Step2: Solve for \(v_2\)

Rearrange the formula: \(v_2 = -\frac{m_1v_1}{m_2}\). Substitute values: \(v_2 = -\frac{0.410\,\text{g} \times 6.50\,\text{m/s}}{13.0\,\text{g}}\). Calculate: \(v_2 = -\frac{2.665}{13.0} \approx -0.205\,\text{m/s}\). The negative sign indicates direction, speed is magnitude.

Answer:

\(0.205\)