You and your friends are doing physics experiments on a frozen pond that serves as a frictionless, horizontal surface. Sofia, with mass 80.0 kg, is given a push and slides eastward. Elena, with mass 55.0 kg, is sent sliding northward. They collide, and after the collision, Sofia is moving at 39.0 ∘ north of east with a speed of 6.40 m/sm/s and Elena is moving at 20.0 ∘ south of east with a speed of 9.40 m/s.
a. What was the speed of each person before the collision?
b. By how much did the total kinetic energy of the two people decrease during the collision?

a)  V_ei = 2.6434 m/s , V_si = 11.05 m/s

b) Loss K.E = 1007.958 J

Explanation:

Given:

- Mass of Sofia Ms = 80 kg

- Mass of Elena Me = 55 kg

- The initial velocity of Sofia = V_si

- The initial velocity of Elena = V_ei

- The final velocity of Sofia V_sf = 6.4 m/s

- The final velocity of Elena V_ef = 9.4 m/s

- The angle sophia makes with east direction towards north θ_1 = 39°

- The angle Elena makes with east direction towards south θ_2 = -20°

Find:

a. What was the speed of each person before the collision?

b. By how much did the total kinetic energy of the two people decrease during the collision?

Solution:

- Since no eternal forces are acting on either Sophia or Elena, then the momentum of both is conserved in all directions.

- Using conservation of momentum in north-south direction. Taking north as positive and south as negative:

                      Me*V_ei = Me*V_ef*sin(θ_2) + Ms*V_sf*sin(θ_1)  

Plug values in:

                      55*V_ei = 55*(9.4)*sin(-20) + 80*6.4*sin(39)

                      55*V_ei = 145.38762

                      V_ei = 2.6434 m/s

- Using conservation of momentum in east-west direction. Taking east as positive and west as negative:

                      Ms*V_si = Me*V_ef*cos(θ_2) + Ms*V_sf*cos(θ_1)

Plug values in:

                      80*V_si = 55*(9.4)*cos(-20) + 80*6.4*cos(39)

                      80*V_si = 883.71981

                      V_si = 11.05 m/s

- The total kinetic energy of both elena and sophia before collision is given by:

                     K.E_i = 0.5*Me*V_ei^2 + 0.5*Ms*V_si^2

                     K.E_i = 0.5*55*2.6434^2 + 0.5*80*11.05^2

                     K.E_i = 5076.258 J

- The total kinetic energy of both elena and sophia after collision is given by:

                     K.E_f = 0.5*Me*V_ef^2 + 0.5*Ms*V_sf^2

                     K.E_f = 0.5*55*9.4^2 + 0.5*80*6.4^2

                     K.E_f = 4068.3 J

- The loss in kinetic energy after collision is given by:

                    Loss K.E = K.E_i - K.E_f

                    Loss K.E = 5076.258 - 4068.3

                    Loss K.E = 1007.958 J

the moon affects the earth gravitation ally, causing certain motions of that body and also producing tides in its ocean and atmosphere. the tidal wave in our atmosphere is, however, far too minute to be an effective cause in any known meteorological phenomenon.

explanation:

1 the 4 is sig