Miles Tugo and Ben Travlun are riding in a bus at highway speed on a nice summer day when an unlucky bug splatters onto the windshield. Miles and Ben begin discussing the physics of the situation. Miles suggests that the momentum change of the bug is much greater than that of the bus. After all, argues Miles, there was no noticeable change in the speed of the bus compared to the obvious change in the speed of the bug. Ben disagrees entirely, arguing that that both bug and bus encounter the same force, momentum change, and impulse. Who do you agree with

Ben os ok. the moment of the bus and the worm are conserved

Explanation:

System formed by the bus and the worm, therefore the forces during the collision are internal and therefore the moment is conserved

initial instant. Airs of shock

        p₀ = My v₀

final instant. After the shock

        p_f = (M + m) v

the moment is preserved

        p₀ = p_f

        M v₀o = (M + m) v

       v =  v₀

       v =  v₀

Let's analyze these equations the moment of the bus and the worm are conserved, therefore Ben is the one who is right. Let us propose the solution of the problem.

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west