- #1
Rijad Hadzic
- 321
- 20
Homework Statement
A circus cat has been trained to leap off a 12 m high platform and land on a pillow. The cat leaps off at [itex] v_0 = 3.5 m/s [/itex] at an angle of 25 degrees. Where should the trainer place the pillow so that the cat lands safely? What is the cats velocity as she lands on the pillow?
Homework Equations
[itex] \Delta x = (1/2)(V_{0x} + V_x)t [/itex]
[itex] \Delta x = V_{0x}t + (1/2)a_x t^2 [/itex]
The Attempt at a Solution
So I calculated [itex] V_{0y} = 3.5sin(25) = 1.479163916 m/s [/itex]
and
[itex] V_{0x} = V_x = 3.5cos(25) = 3.172077255 m/s [/itex]
So there are two times here,
what I will call [itex] t_1 [/itex] = time it takes from start of movement to very top, and then back down, so a [itex] \Delta y [/itex] displacement of 0.
[itex] t_2 [/itex] = From the above, the second part, starting when the y displacement hits 0, to when the cat lands on the pillow.
I use equation [itex] V_{0x} + a_x t [/itex] to find [itex] t_1 [/itex]
Since I know the inital y velocity = 1.479163916, I know that at the point I'm talking about, after it goes up and comes back down to a [itex]\Delta y [/itex] of 0, the velocity is going to be the same magnitude but opposite direction, so final y velocity = -1.479163916
solving for t I get
[itex] t_1 = (-1.479163916 - 1.479163916 ) / -9.8 = .3018701869 [/itex]
Does this make sense so far?
Now I have to get [itex] t_2 [/itex] so I use formula: [itex] \Delta y = V_{0y}t + (a_y/2)t^2 [/itex]
with [itex] V_{0x} = -1.479163916 m/s [/itex] since we are starting AFTER [itex] t_1[/itex], [itex] a_x/2 = -4.9 m/s^2 [/itex] and [itex] \Delta y = 12 m [/itex]
Now I want to use the quadratic equation to get my t here, but under the square root I get a negative value. my quadratic looks like:
[itex] -V_{0y} {+-} \sqrt {V_{0y}^2 -4(a_y/2)(-\Delta y)} [/itex] all divded by [itex] a_y [/itex]
is what my quadratic looks like. Plugging the values I listed above for the variables, I get a - inside my sqroot which makes no sense to me. I realize that this IS the way to go about this problem though, I just don't understand what I did wrong from here?
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