An 1810-kg truck traveling eastward at 64.4 km/h collides at an intersection with a 905-kg automobile traveling northward at 96.5 km/h. The vehicles lock together and immediately after the collision are headed in which direction?

Question

Quizplus · Accepted Answer

The correct answer is B) 37° N of E.Explanation:The momentum of the truck is:$$P_t = m_t v_t = (1810 	ext{ kg})(64.4 	ext{ km/h}) = 116,284 	ext{ kg m/s}$$The momentum of the automobile is:$$P_a = m_a v_a = (905 	ext{ kg})(96.5 	ext{ km/h}) = 87,218 	ext{ kg m/s}$$The total momentum of the system is:$$P = P_t + P_a = 116,284 	ext{ kg m/s} + 87,218 	ext{ kg m/s} = 203,502 	ext{ kg m/s}$$The angle of the total momentum is:$$	heta = 	an^{-1}\left(\frac{P_a \sin 90^\circ}{P_t + P_a \cos 90^\circ}ight) = 	an^{-1}\left(\frac{87,218 	ext{ kg m/s}}{116,284 	ext{ kg m/s}}ight) = 37^\circ$$Therefore, the vehicles lock together and immediately after the collision are headed in the direction of 37° N of E.

An 1810-Kg Truck Traveling Eastward at 64