Question

In this question we handle a one dimensional elastic collision. Thus, suppose that the mass m, bearing the velocity VIP collides with the mass ml, initially at rest. After the collision, and my acquire the velocities, respectively, vi and v2f. a) (15 p) Therefore, show these two equations: my - m2 2m Vir Vu V2r- VU my+m2 m+ m2 b) (10p) Suppose, a bus running at the velocity of 100 km/h, hits a cow, on the highway. What would be the speed of the bus after the collision. And, what would be the speed of the cow after the given collision? +

Answer 1

(a) The given collision is one dimensional elastic collision. Hence, here kinetic energy momentum leoth and wire le conserved. Man = m2 Mass ami Initial Final relocity = Vif V Te + m2 vef If 2 ون relocity - Vii Initial velocity Vzi = 0 final relocity = V2f from the conservation of kinetic energy, Initial kinetic Energy = final kinetic energy ₂ mi + 2 M2 Vai = ² m muit = mini + Mz rze (iv?i=0) (1) From the conservation of momentum, final Juilial momentum = momentum mivit my vri = (mi vip) +(m_2 VID) marif travel 24 mi cvii - Vif) -(2) (2) in (1) we mp (Vic-Vig)? m₂ (vii-44) m, Cvictv ma (Vic-UP)? ☺ mivii us me Pulting (2) in movie m2 (1) we get mivi mi (vie (v-v%) 14) (Vi-vif) u my 2 ๆ m₂

w 3 (Vic+Vif) m. s (Yri-lif Vii vii m 1 1 vif - Vif Voir moins vie (en en) -) Vi ♡ mi f if zus m₂ m, mz mitm2 = vif Vif mz m2 Vif mi-mz Vii mitm2 (paroad) Putting this value of of Vif in (2) we get, mi m2 "2f mz Vii [ vil] "li mitmz V2f em-lue my Vii m2 zutlue 2 mi ten = vie (Proved) matm2

cow are the cow -b) Mass of the bus and not provided here let the mass of the bus мь mans of the = Mc As the problem is associated with its previous Part we can take the initial velocity of the cow 21 Initial velocity of the bus = 100 km/h =vi From the above proven expressions we can say that the speed of the bus after collision is M6-Mc - v: - O vif { Mbt Me .) x 100 km/h the speed of of the cow after the collision is Vzq = {( 2 ) roo} kufu If the calculate masses are provided both the velocities we can in km/h. (speede)