Small-plane pilots regularly compete in "message drop" competitions, dropping heavy weights (for which air resistance can be ignored) from their low-flying planes and scoring points for having the weights land close to a target. a plane 70 m above the ground is flying directly toward a target at 44 m/s . at what distance from the target should the pilot drop the weight?

plane is flying at an altitude of 70 m

now if an object is dropped from it then time taken by object to drop on ground will be given as

here initial speed in vertical direction must be zero as plane is moving horizontal

given that

y = 70 m

a = 9.8 m/s^2

now since the plane is moving horizontally with speed v = 44 m/s

so the horizontal distance moved by the object will be

so the distance moved by the box is 166.3 m

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.