the final speed in m/s of the 10.0 kg is 2.53 m/s .
Step-by-step explanation:
Here we have , A 10.0 kg and a 2.0 kg cart approach each other on a horizontal friction less air track. Their total kinetic energy before collision is 96 ). Assume their collision is elastic. We need to find What is the final speed in m/s of the 10.0 kg mass if that of the 2.0 kg mass is 8.0 m/s . Let's find out:
We know that in an elastic collision :
⇒ Total kinetic energy before collision = Total kinetic energy after collision
⇒ [tex]96 = \frac{1}{2}M_1(v_1)^2 + \frac{1}{2}M_2(v_2)^2[/tex]
⇒ [tex]96 = \frac{1}{2}(10)(v_1)^2 + \frac{1}{2}(2)(8)^2[/tex]
⇒ [tex]96=5(v_1)^2 + 64[/tex]
⇒ [tex]5(v_1)^2 =32[/tex]
⇒ [tex](v_1)^2 =6.4[/tex]
⇒ [tex]v_1 =2.53 m/s[/tex]
Therefore , the final speed in m/s of the 10.0 kg is 2.53 m/s .
