In example 2.12, two circus performers rehearse a trick in which a ball and a dart collide. horatio stands on a platform 6.4 m above the ground and drops a ball straight down. at the same moment, amelia uses a spring-loaded device on the ground to launch a dart straight up toward the ball. the dart is launched at 16.2 m/s. find the time and height of the collision by simultaneously solving the equations for the ball and the dart. (due to the nature of this problem, do not use rounded intermediate values in your calculations—including answers submitted in webassign.)

time of collision is

t = 0.395 s

so they will collide at height of 5.63 m from ground

Explanation:

initial speed of the ball when it is dropped down is

similarly initial speed of the object which is projected by spring is given as

now relative velocity of object with respect to ball

now since we know that both are moving under gravity so their relative acceleration is ZERO and the relative distance between them is 6.4 m

Now the height attained by the object in the same time is given as

so they will collide at height of 5.63 m from ground

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.