A pair of skydivers jump out airplane 5.5km above the ground. The equation H=5500-5t^2 is an appropriate model for the divers' altitude in metres at tseconds after jumping out of the plane.
A. After 10secs how far have the divers fallen?
B. They open their chutes at an altitude of 1000metres. how long did they free-fall?
C. If a parachute does noe open at 1000metres,how much time is left to use the emergency chute?
For (a),I got H=5000 and (b), I got t=30secs
BUT i do not know how to get the answer for QUESTION (C).
PLS HELP ME ,HAVE TRIED IT BUT I DIDN'T GET IT.
Find out how long it would take to fall the entire 5500 m
so
0 = 5500 - 5t^2
t^2 = 1100
t = 33.167 sec
but he has already fallen for 30 sec , so he has
3.167 sec left
To find the answer for question (C), we need to determine the time it takes for the divers to reach an altitude of 1000 meters and subtract it from the total time since they jumped out of the plane.
Given that the equation for the divers' altitude is H = 5500 - 5t^2, we can set H equal to 1000 and solve for t:
1000 = 5500 - 5t^2
Rearranging the equation, we get:
5t^2 = 5500 - 1000
5t^2 = 4500
Dividing through by 5, we have:
t^2 = 900
Taking the square root of both sides, we get:
t = √900
t = 30
So it takes 30 seconds for the divers to reach an altitude of 1000 meters. Since they opened their chutes at this altitude after 30 seconds, the remaining time after opening the chutes is:
Total time since jumping - Time to reach 1000 meters = 10 seconds - 30 seconds = -20 seconds
Since -20 seconds does not make sense in this context, it means that the divers will not have any time left to use the emergency chute if the main parachute does not open at 1000 meters.
To find the answer to question (C), we need to determine how much time is left to use the emergency chute if the main parachute does not open at 1000 meters.
First, let's set up an equation to represent the scenario. Since the altitude at any time t is given by the equation H = 5500 - 5t^2, we can equate H to 1000 and solve for t.
1000 = 5500 - 5t^2
Rearranging the equation, we have:
5t^2 = 5500 - 1000
5t^2 = 4500
Dividing both sides by 5, we get:
t^2 = 900
Taking the square root of both sides, we find:
t = sqrt(900)
t = 30
So, at an altitude of 1000 meters, the time elapsed since jumping out of the plane is 30 seconds.
Now, to determine how much time is left to use the emergency chute, we need to subtract the time elapsed from the total free-fall time.
Given that the total free-fall time is 30 seconds (from part (b)), we subtract the time elapsed (30 seconds) from the total free-fall time:
Time left = Total free-fall time - Time elapsed
Time left = 30 seconds - 30 seconds
Time left = 0 seconds
Therefore, if the main parachute does not open at 1000 meters, there is no time left to use the emergency chute.