If the speed of a roller coaster at the bottom of a hill is 20.0 m/s , what is the tallest hill the coaster can climb, assuming no friction losses ?

20.4 meters

Explanation:

KE = 1/2 m v^2 = mgh = PE (convert all kinetic energy to potential energy, because at the highest point the coaster can climb, it will be stopped!)

=> h = (1/2 m v^2) / (mg) = v^2/(2*g) = (20 m/s)^2 / (2*9.8 m/s^2) = 20.4 m

answer: (431,2)

step-by-step explanation:

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.