An ice cube of mass 50.0 g can slide without friction up and down a 25.0 degree slope. The ice cube is pressed against a spring at the bottom of the slope, compressing the spring 0.100 m . The spring constant is 25.0 N/m . When the ice cube is released, how far will it travel up the slope before reversing direction?

d = 0.604 m

Explanation:  set 0 GPE at max spring compression, then

total E = U =  1/2kx^2 = 1/2 25N/m (0.1m)^2  = 0.125 J

max height,

GPE = 0.125 J = mgh = 0.05kg 9.8m/s^2 h

h = 0.255 m

Along slope,  d = 0.255m / sin25°

d = 0.604 m

It's possible they want the distance from the end of the spring -- that's 0.504 m

f=ma a/f/m a= 480/60 a = 8m/s/s that is quick wow

answer: at 24 february, 2014 the population gets twice of its initial population.

explanation:

since we have given that

the population for alpha city, t years after january 1, 2004 is given as

first we find out the initial population, i.e. t=0,

so, our quadratic equation becomes,

according to question, we have said that if the population has twice its initial population, then it becomes

so, time taken to reach this above mentioned population is given by

now, we know that time can't be negative so, we take t=9.149 years.

hence, at 24 february, 2014 the population gets twice of its initial population.