Respuesta :
Answer:
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
