hey, got an assignment due VERY soon should have done it earlier was too busy riding.
can anybody please help me work this out.
Task2:
The pilot of a small plane is attempting to land on a small airstrip, and the wheels hit the runway only 1000 metres short of a large group of trees at the end of the runway. The plane’s speed on the tarmac is modeled by the equation v = A-10^kt, where v the plane’s velocity in m/s, t is the time taken n seconds to come to a complete halt and A and K are constants.
graph showing decelleration of plane
If the pilot is attempting to land the plane at a speed of 80m/s,
a. Calculate the value of A (1 mark)
b. 8) investigate at least 3 different values of k between (but not including) 0.01 and 0.2 and for each value determine whether the plane comes to a complete stop before the end of the runway. Use any graphs and/or diagrams, any numerical techniques and any technology t
to support your arguments, justify your procedures. What physical conditions could make k vary? List assumptions you have made. Would there be any values of k (not just the values between 0.01 and 0.2) for which this equation could not be used to model the velocity of a plane landing on a tarmac? Give your reasons and justify your answer
Just to verify, is it v = A - 10 to the power of (k times t) or is it v = A - (10 to the power of k) times t? The first one would be very strange and give a very unrealistic graph for deceleration. Is t 0 at touch-down? Could you post the exact wording from the text-book?
Edit: On a second thought, I’m not sure how realistic the graph would be. I guess it depends how the plane decelarates. If it’s by reversing the turbines then it wouldn’t be that bad, I guess.
a) I think A will be 81 m/s. V should be 80m/s at touch-down(specified), so.
v = A - 10^kt => 80m/s + 10^(k0) = 81m/s. This would really make much more sense(to me, at least) if it was something like t10^k, but there we are.
they ave us a graph that has time down the bonnom, which goes for 16 units, and no label on the y axis. there is a curse from the top left to the bottom right.
Yes, I think so. Now you either have to have a graph for each value of k that you’re testing and find the area under it by counting the squares(the old one) or integrate v=A - 10^kt and find the area between t=0 and t when v is 0. I’m still trying to figure out how to integrate the thing, can’t think of a way.
Well, you could do it manually. Are you allowed calculators? Or you could also use the trapezium rule to find an estimate. I can’t believe I didn’t think of this before. That’s probably the easiest solution in this situation.
