The distance in feet that a skydiver is from the ground (t) seconds after jumping from an airplane flying at 17,000 ft above ground is given by the following equation: d(t)=-16t^2 +17000. a.) how many feet above ground is the skydiver above ground after 4 seconds? b.)how many seconds have past when the skydiver reaches 3000 ft
a) just plug in 4 for t and evaluated,
remember to square first, that is,
-16(16) + 17000
b) set 3000 = -16t^2 + 17000
16t^2 = 14000
t^2 = ± √14000/4
= appr 29.6 sec. , obviously ignoring the negative.
(not realistic, skydivers do not fall according to that formula)
a) To find the distance above the ground after 4 seconds, we need to substitute t = 4 into the equation d(t) = -16t^2 + 17000:
d(4) = -16(4)^2 + 17000
d(4) = -16(16) + 17000
d(4) = -256 + 17000
d(4) = 16744
Therefore, the skydiver is 16,744 feet above the ground after 4 seconds.
b) To find the time when the skydiver reaches 3,000 feet above the ground, we need to solve the equation -16t^2 + 17000 = 3000 for t. Rearranging the equation, we have:
-16t^2 + 17000 = 3000
-16t^2 = 3000 - 17000
-16t^2 = -14000
Divide by -16 to solve for t:
t^2 = 14000/16
t^2 = 875
Taking the square root of both sides:
t = √(875)
t ≈ 29.58
Therefore, it takes approximately 29.58 seconds for the skydiver to reach a height of 3000 feet.
To find the distance in feet that a skydiver is from the ground at a specific time, we can substitute the given time value into the equation d(t) = -16t^2 + 17000.
a) To find the height after 4 seconds, we substitute t = 4 into the equation:
d(4) = -16(4)^2 + 17000
d(4) = -16(16) + 17000
d(4) = -256 + 17000
d(4) = 16744
Therefore, the skydiver is 16,744 feet above the ground after 4 seconds.
b) To find the time when the skydiver reaches 3000 feet, we need to solve the equation -16t^2 + 17000 = 3000.
First, we rearrange the equation:
-16t^2 + 17000 - 3000 = 0
-16t^2 + 14000 = 0
Next, we solve for t by factoring or using the quadratic formula.
Factoring the equation:
-16(t^2 - 875) = 0
Setting each factor equal to zero:
t^2 - 875 = 0
Using the difference of squares:
(t - sqrt(875))(t + sqrt(875)) = 0
Setting each factor equal to zero and finding the square root of 875:
t - sqrt(875) = 0 or t + sqrt(875) = 0
t = sqrt(875) or t = -sqrt(875)
Since time cannot be negative, we discard the negative value. Therefore:
t = sqrt(875)
Using a calculator, we find that sqrt(875) ≈ 29.58.
Therefore, the skydiver reaches 3000 feet after approximately 29.58 seconds.