Question

a 1425 kg truck driving at 13.0 m/s collides elastically with a stationary 1175 kg car. if the car is traveling 14.25 m/s just after the collision, what is the velocity of the truck immediately after the collision? assume that this is a perfectly elastic collision. round your answer to the hundredths place. final velocity of the truck = m/s

Explanation:

Step1: Apply the conservation of momentum

The formula for conservation of momentum is \(m_1u_1 + m_2u_2=m_1v_1 + m_2v_2\). Here, \(m_1 = 1425\space kg\), \(u_1=13.0\space m/s\), \(m_2 = 1175\space kg\), \(u_2 = 0\space m/s\), \(v_2=14.25\space m/s\). Substitute these values into the formula:
\(1425\times13.0+1175\times0 = 1425v_1+1175\times14.25\)
\(18525=1425v_1 + 16743.75\)

Step2: Solve for \(v_1\)

Rearrange the equation from Step 1 to solve for \(v_1\):
\(1425v_1=18525 - 16743.75\)
\(1425v_1 = 1781.25\)
\(v_1=\frac{1781.25}{1425}\)
\(v_1 = 1.25\space m/s\)

Answer:

\(1.25\space m/s\)