Question

A 402.89 kg van traveling at 20.54 m/s rear-ends an 704.44 kg compact car going 26.62 m/s. If the two vehicles stick together what will be their new speed?

Answer 1

Given data

*The given mass of the van is m = 402.89 kg

*The initial speed of the van is u_1 = 20.54 m/s

*The given mass of the compact car is M = 704.44 kg

*The initial speed of the compact car is u_2 = 26.62 m/s

The formula for the new speed of both the vehicles is given by the conservation of momentum as

`\begin{gathered} p_i=p_{f_{}} \\ mu_1+Mu_2=(m+M)v_{}_{} \\ v=(mu_1+Mu_2)/((m+M)) \end{gathered}`

Substitute the known values in the above expression as

`\begin{gathered} v=((402.89*20.54)+(704.44*26.62))/((402.89+704.44)) \\ =24.40\text{ m/s} \end{gathered}`

Hence, the new speed of both the vehicles when they stick together is v = 24.40 m/s