math high school?
A skydiver jumps from an airplane at an altitude of 3000 m. As long as his parachute is still closed, his falling speed can be approximately described by a function v with (t in seconds from jump, v(t) in m/s):
v(t)=49 • (1-e^-0.2t)
a) Calculate the falling speed 6 seconds after take-off.
b) Calculate the time at which the jumper has a speed of 40 m/s.
c) Calculate the instantaneous rate of change of speed (=acceleration) 2 seconds after take-off.
I need help calculating this…
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First, make sure what the function brings you. You have two variables here. Once the speed v and the time t. So if you have given a time, you can calculate the speed at this time.
You can also calculate the times at which you have a certain speed. You have to use the given value.
And that's how you already calculate tasks a) and b).
For c), you only need the information that the derivation of speed is the acceleration. Thus, derive once and subsequently the same principle as in (a) and (b).
What kind of help do you need when you're in high school? I hope you'll be able to calculate v(6), right? For the dissolved v(t) = 40 after t. For the c derive v after t and calculate v'(2).