Question

Some object falls off a tower. A flying cat at the top of the tower flies down 3 sec later to catch the object. The cat's initial v = 500 cm/s and constant acceleration = 1400 cm/s^2. what is the time it takes for the flying cat to catch the object? how far does the object fall before it gets caught by the cat?

Answer 1

Given that the acceleration is = 1400 and Since the acceleration function a(t) is the rate of change of the velocity function v(t) then we can say that ∫a(t)dt= v(t). Therefore v(t) = 1400t+c. Since the cats initial velocity is 500 cm/s and he was 3 seconds late then we can say that v(3) = 500 or -3700 = c. So v(t) = 1400t-3700. The position function p(t) for the cat is then p(t) = 1400t^2 -3700t + c. If we make the position at the top of the tower 0 then p(3) = 0 and c = -1500 making p(t) = 1400t^2 -3700t - 1500 For the object, if we are assuming that the object is falling on earth, then the acceleration a(t) = 980 cm/s^2. v(t) is then v(t) = 980t+c. Assuming the initial velocity at time t = 0 is 0 then v(0) = 0 and c = 0 and v(t) = 980t. p(t) for the object is p(t) = 980t^2 + c. p(0) = 0 so c = 0 and p(t)= 980t^2. set them equal and 980t^2 = 1400t^2 -3700t - 1500. solve for t by subtracting 980t^2 from both sides then 0 = 420t^2 -3700t - 1500 or 0 = 42t^2 -370t - 150. use the quadratic formula and t = 5/42 (37+sqrt(1621)).

Answer 2

It's a trick question. Cats can't fly. ;)

Answer 3

@eighthourlunch no further comments?

Answer 4

Ha! Sorry, no. I shouldn't have answered that much, I'm supposed to be helping with dinner.

Answer 5

thanks
But shouldn't p(t) = 490t^2? and p(t) for superman 700t^2 +......

Answer 6

Ah @Algebraic! found a mistake in my calculations. The position equation for the cat should be 700t^2 -3700t - 1500 and the position equation for the object should be 490t^2 making t = 5/21 (37+sqrt(1495))

Answer 7

@FishingWithTNT yes sorry about that.

Answer 8

oops messed up again, forgot to solve for c with the new equations. I think you get the gist of what I was trying to do though?

Answer 9

yeah I got it! thanks