Question

In this question we handle a one dimensional elastic collision. Thus, suppose that the mass m, bearing the velocity v collides with the V li mass m2, initially at rest. After the collision, m , and m, acquire the velocities, respectively, and v Vif v2f a) (15 p) Therefore, show these two equations: 2m Di mi-m2 mi+ m2 Vii 1 V2= mi+m2 b) (10 p) 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

Page No. (a) Initial Initial total momentum m, vit m₂ + m₂ o → P: m. vii = final total momentum m. vif + Ma Vaf m, vif t Pf M₂ V 2f By conservation of momentum Ps Pf Pi + Mg Vaf = mivi mi vif elastic , therefore kinetic energy १ Since collision is is also conserved :kf Eki I m, vif + I 2 - ma ve if Imivi * m vit ma v f = m vi (2)

w) = m2 m2 V2f 2 2 from eqn m (Mii -V.p.) from eg" mi (v vi (4 6 gives Vi tvif. » Vzf=vitvif m2 y 2 Vaf 3 non V2f 5 Substituting V2f ins mi vif + m2 (vii tvif) m vil = m, Vif + m2 Vii + m2 Vif mivi > Nif m, time) m, - m2) vi mi-m2 . Vif Vi mitm2 Substit this in 5 tituting Vif

2 ml 1л ҒА Л Ime mitm2 2 mitm2 Vi vi Niit FA С (А4 -- 'м, The —