# SOLUTION: Skydiving. If there were no air resistance, then the height (in feet) above the earth for a skydiver t seconds after jumping from an airplane at 10,000 feet would be given by h(t)

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 Click here to see ALL problems on Distributive-associative-commutative-properties Question 123536This question is from textbook Elementary and intermediate Algebra : Skydiving. If there were no air resistance, then the height (in feet) above the earth for a skydiver t seconds after jumping from an airplane at 10,000 feet would be given by h(t)= -16t^2 + 10,000 a) find the time that it would take to fall to earth with no air resistance: that is, find t for which (t)= 0.A skydiveractually gets about twice as much free fall time due to air resistance. b)Use the accompanying graph to determine whether the skydiver(with no air resistance ) falls farther in the first 5 seconds or the last 5 seconds of the fall. c) Is the skydiver's velocity increasing or decreasing as she falls?This question is from textbook Elementary and intermediate Algebra Found 2 solutions by stanbon, rajagopalan:Answer by stanbon(57282)   (Show Source): You can put this solution on YOUR website!If there were no air resistance, then the height (in feet) above the earth for a skydiver t seconds after jumping from an airplane at 10,000 feet would be given by h(t)= -16t^2 + 10,000 a) find the time that it would take to fall to earth with no air resistance: that is, find t for which (t)= 0.A skydiveractually gets about twice as much free fall time due to air resistance. When on earth the height is zero. -16t^2+10,000=0 -16t^2 = -10,000 t^2 = 625 t = 25 seconds ---------------------------- b)Use the accompanying graph to determine whether the skydiver(with no air resistance ) falls farther in the first 5 seconds or the last 5 seconds of the fall. Height after 5 seconds = h(5)=-16(5^2)+10000 = 9600 ft The skydiver falls 400 ft in the 1st 5 seconds. ------------------ Height after 20 seconds = h(20)=-16(20^2)+10000= 3600 ft Height aftrer 25 seconds is zero The skydiver falls 3600 ft in the last 5 seconds. ----------------------- c) Is the skydiver's velocity increasing or decreasing as she falls? increasing. =============== Cheers, Stan H. Answer by rajagopalan(158)   (Show Source): You can put this solution on YOUR website!Part aaa. Skydiving. height (in feet) above the earth=h(t)= -16t^2 + 10,000 the time it would take to fall when h is 0 -16t^2 + 10,000=0 -16t^2=-10000 16t^2=10000 t^2=10000/16=625 t=sqrt 625=25 seconds okay Part bbb)Use the accompanying graph to determine whether the skydiver(with no air resistance ) falls farther in the first 5 seconds or the last 5 seconds of the fall. Though no graph is given we can calculate this: Fall distance in first 5 sec =-16t^2 =-16(5*5)=-16*25=-400 m =400 m Fall distance in Last 5 sec =ht after 25 sec-ht after 20 sec ht after 25 sec=-16t^2 + 10,000=-16(25*25)+10000=-10000+10000=0 ht after 20 sec=-16t^2 + 10,000=-16(20*20)+10000=- 6400+10000=3600 m So in the Last 5 secs he falls thro 3600 m as against 400m in the first 5 secs. Part ccc) Is the skydiver's velocity increasing or decreasing as she falls? Mean Velocity in first 5 secs =dist/time=400/5=80 m/sec Mean Velocity in Last 5 secs =dist/time=3600/5=720 m/sec Obviously Velocity is increasing. In fact he is accelerating. Note : Ignore the signs for distance as descending is shown as negative. Cheers good day