Question

At the intersection of Texas Avenue and University Drive, a yellow subcompact car with mass 950 kg traveling east on University collides with a red pickup truck with mass 1900 kg that is traveling north on Texas and has run a red light (Fig. E8.41). The two vehicles stick together as a result of the collision, and the wreckage slides at 16.0 m/s in the direction 24.0° east of north. Calculate the speed of each vehicle before the collision. The collision occurs during a heavy rainstorm; ignore friction forces between the vehicles and the wet road.

Answer 1

In order to solve this problem it is necessary to apply the conservation equations of the moment, specifically when it comes to problems of inelastic collision. The equation is given by,

$m_1v_1+m_2v_2 = (m_1+m_2)v_f$

Since the problem is about an intersection, it is necessary to consider the velocity components for each one,

In the case of the car, if we define it on the vertical component we would have to,

$m_1v_1 = (m_1+m_2)vsin\theta$

$v_1 = \frac{(m_1+m_2)vsin\theta}{m_1}$

$v_1 = \frac{(950+1900)(16)(sin(24))}{950}$

$v_1 = 19.523m/s$

Therefore the velocity of the car before the collision is 19.523m/s

In the case of the truck we apply the velocity formula in the x component, then we would have,

$m_2v_2 = (m_1+m_2)vcos\theta$

$v_2 = \frac{(m_1+m_2)vcos\theta}{m_2}$

$v_2 = \frac{(950+1900)(16)(cos(24))}{1900}$

$v_2 = 21.925m/s$

Therefore the velocity of the truck before the collision is 21.9m/s