Please Help!! In an elastic head-on collision, a 0.60 kg cart moving at 5.0 m/s [W] collides with a 0.80 kg cart moving at 2.0 m/s [E]. The collision is cushioned by a spring (k = 1200 N/m). a) Determine the velocity of each cart after the collision. b) Determine the maximum compression of the spring.

initial momentum 0.6kg * -5m/s + 0.8kg * 2m/s = -1.4 kg·m/s

final momentum = -1.4 kg·m/s = 0.6kg * u + 0.8kg * v

For an elastic head-on collision, we know that the

relative velocity of approach = relative velocity of separation, or

7m/s = u - v, or

u = v + 7

Plug this into momentum eqn:

-1.4 = 0.6(v+7) + 0.8v = 0.6v + 4.2 + 0.8v

-5.6 = 1.4v

v = -4 m/s ← 0.8kg cart, now moving West

u = v + 7 = 3 m/s ← 0.6kg cart, now moving East

initial Ek = ½ * 0.6kg * (5m/s)² + ½ * 0.8kg * (2m/s)² = 9.1 J

This gets converted into spring energy,

U = 9.1 J = ½kx² = ½ * 1200N/m * x²

x = 0.123 m = 12.3 cm

i had this question and the answer was 3.15 miles.

martina travels from school to her mom's office. from there, she walks to school. after school, she walks to the library and then to a friends house before finally ending back at home. find martina's total distance traveled.

a) 0 miles  

b) 0.4 miles  

c) 1 mile  

d) 3.15 miles