Question

In this question we handle a one dimensional elastic collision. Thus, suppose that the mass m₁ bearing the velocity v_1i, collides with the mass m₂, initially at rest. After the collision, m₁ and m₂ acquire the velocities, respectively, v_1f  and v_2f.

a) Therefore, show these two equations:

b) 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

move det two particles of mass my and m2 with velocities ūs, ūa respectively. and after Collision velocities become V J respectively. From Conservation of momentum mie, tm₂42 = mie + m₂ U₂ or, m, (",-VI) = m₂ (U2-U2) -(1) since again, Collision is elastic Conservation of KoE. 2 m, 4,²+1 / m₂ 4 = 1 m, v, 2+1 m₂ vez ap, mq (1,7-1, 2) = m₂ (V2 - 42 ) - - (2) Dividing (2) by (1) Ust u U2+U₂ - (3) Putting value of v2 = 4, + - U₂ in eqh (1) 2 we get U₂ m, -m₂ 2 m2 .lt metm2 my t mq Similarly V2 = m2-mi -U2+ m, the m, tha 2m. us. 6) a)) In our Vi Case relocities are Vaf Vai Vaf So equation (4) & (5) becomes m,.mz Vef Vit mitm₂ am2 • Vai m, tm2 m, m2-my Vaf = Vzit m, tm, mitma Vai CS Scanned with CamScanner

b) Let velocity of bus. Vai = 100 km/h = 105 mis Initial velocity of cow =Vzi=0 (rest) 3650 =100x 5 m/s 18 here mi >> m2 Vif ma - _miz m, +mg 2 m2 Viit Vei mitm, or. Vyf = ma mi -Vi = 100 kn/h neglecting mass of cow. w.pit mass of buy. Vaf = m₂-m, mitm2 am Vai + Vsi m, tm2 2 m ot my Vsi - . 2 xloo = 200km/h Velocity of the bus remain same 1 o okmilh. velocity of Cow after collission becomes 2.00 km/h and ® please give a nating will help me. Comment an any doubt sure help. CS Scanned with CamScanner