Question

1. while bow hunting, dan sees a monster buck approaching. dan realizes he left his bow in his truck and attempts to tackle the deer by running after it. if he gains a momentum of 350 kg·m/s while running at a speed of 5.8 m/s, what is dans mass?
2. in a collision, a 15 kg object moving with a velocity of 3 m/s transfers all of its momentum to a 5 kg object. what would be the velocity of the 5 kg object after the collision? (hint: think about the law of conservation of momentum and draw a picture of what is happening)
3. a linebacker with a mass of 100 kg moving at 5 m/s transfers all his momentum to a quarterback. if the quarterback is sent to the ground with a velocity of 6.5 m/s, what is his mass? (hint: think about the law of conservation of momentum and draw a picture of what is happening)

Explanation:

Step1: Recall the momentum formula

Momentum \(p = mv\), where \(p\) is momentum, \(m\) is mass, and \(v\) is velocity. We need to solve for \(m\) when \(p = 350\space kg\cdot m/s\) and \(v=5.8\space m/s\). Rearranging the formula gives \(m=\frac{p}{v}\).

Step2: Substitute values into the formula

Substitute \(p = 350\) and \(v = 5.8\) into \(m=\frac{p}{v}\), so \(m=\frac{350}{5.8}\).

Step3: Calculate the mass

\(m=\frac{350}{5.8}\approx60.34\space kg\)

Step1: Apply the Law of Conservation of Momentum

The Law of Conservation of Momentum states \(p_1 = p_2\). For the first object, \(p_1=m_1v_1\) where \(m_1 = 15\space kg\) and \(v_1=3\space m/s\). For the second object, \(p_2=m_2v_2\) where \(m_2 = 5\space kg\) and \(v_2\) is the unknown. Since \(p_1 = p_2\), we have \(m_1v_1=m_2v_2\).

Step2: Solve for \(v_2\)

Rearrange \(m_1v_1=m_2v_2\) to get \(v_2=\frac{m_1v_1}{m_2}\). Substitute \(m_1 = 15\), \(v_1 = 3\), and \(m_2 = 5\) into the formula. So \(v_2=\frac{15\times3}{5}\).

Step3: Calculate \(v_2\)

\(v_2=\frac{45}{5}=9\space m/s\)

Step1: Use the Law of Conservation of Momentum

By the Law of Conservation of Momentum \(p_{linebacker}=p_{quarterback}\). For the linebacker, \(p_{linebacker}=m_{linebacker}v_{linebacker}\) with \(m_{linebacker}=100\space kg\) and \(v_{linebacker}=5\space m/s\). For the quarterback, \(p_{quarterback}=m_{quarterback}v_{quarterback}\) where \(v_{quarterback}=6.5\space m/s\). So \(m_{linebacker}v_{linebacker}=m_{quarterback}v_{quarterback}\).

Step2: Solve for \(m_{quarterback}\)

Rearrange \(m_{linebacker}v_{linebacker}=m_{quarterback}v_{quarterback}\) to \(m_{quarterback}=\frac{m_{linebacker}v_{linebacker}}{v_{quarterback}}\). Substitute \(m_{linebacker}=100\), \(v_{linebacker}=5\), and \(v_{quarterback}=6.5\) into the formula. So \(m_{quarterback}=\frac{100\times5}{6.5}\).

Step3: Calculate \(m_{quarterback}\)

\(m_{quarterback}=\frac{500}{6.5}\approx76.92\space kg\)

Answer:

Dan's mass is approximately \(60.34\space kg\)