Rain has velocity v ⃗ \vec{v} v = 10î - 20ĵ m/s. A car starts from rest and accelerates eastward at 5 m/s². In vertical cross-section, its windshield is represented by a straight line of slope -1 with respect to the +x direction. At what time will the rain strike the windshield normally?

Question

G1 Physics · Accepted Answer

At time t, car velocity is v⃗_C = 5t î. Hence relative rain velocity is v⃗_RC = (10 - 5t)î - 20ĵ. A line of slope -1 has a normal of slope +1, so for normal incidence the relative velocity must have equal-sign, equal-magnitude x and y components. Thus 10 - 5t = -20. Therefore 5t = 30 and t = 6 s. Hence option C is correct.