Question

Two 6.7 kg bodies, A and B, collide. The velocities before the collision are and . After the collision, . What are (a) the x-component and (b) the y-component of the final velocity of B? (c) What is the change in the total kinetic energy (including sign)?

Answer 1

Question:

Two 6.7 kg bodies, A and B, collide. The velocities before the collision are
`40i+37j` and
`19 i +3.7 j` . After the collision
`9.8 i + 5.1 j`,
`50 i+35.6 j` . What are (a) the x-component and (b) the y-component of the final velocity of B? (c) What is the change in the total kinetic energy (including sign)?

Answer:

(a) 50 m/s

(b) 35.6 m/s

(c) -735.16 J

Step-by-step explanation:

Given,

`u_A=40i+37j=√(40^2+37^2)=54.5 m/s`

`u_B=19 i +3.7 j=√(19^2+3.7^2)=19.4m/s`

`v_A=9.8 i + 5.1 j=√(9.8^2+5.1^2)=11m/s`

`v_B=50 i+35.6 j=√(50^2+35.6^2)=61.4m/s`

Change in kinetic energy = final kinetic energy - initial kinetic energy

`\Delta K.E.=(1)/(2) m(v_A+v_B)^2 -(1)/(2) m(u_A+u_B)^2\\`

`\Delta K.E.=(1)/(2) 6.7(11+61.4)^2 -(1)/(2) 6.7(54.5+19.4)^2\\\Delta K.E. =17559.89-18295.05\\\Delta K.E. = -735.16 J`