Question

You accidently throw your car keys horizontally at 8.0 m/s form a cliff 64m high. how far from the base of the cliff should you look for the keys

Read more: You accidently throw your car keys horizontally at 8.0 m/s form a cliff 64m high. how far from the base of the cliff should you look for the keys?

Answer 1

Solve for time first, \[y=y_0 +v_yt+\frac{1}{2}g t^2\] Since your velocity is zero from the start of the drop your equation looks like this:\[0=64m + 0 + \frac{1}{2}\times 9.8\frac{m}{s^2} \times t^2\]\[\sqrt{\frac{2 \times -64m}{9.8\frac{m}{s^2}}}=t \rightarrow t= 3.6s\] Now solve for your x: \[x=x_0 +v_xt+\frac{1}{2}g t^2\]\[x=0+(8.0\frac{m}{s} \times 3.6s) + (\frac{1}{2} \times 9.8\frac{m}{s^2} \times 3.6s^2) \rightarrow x=92.3m\]

Answer 2

great answer eSpex (a little mistake - the accelration in the x axis is zero! not g). What is nice about that question is that the movement down (y axis - free fall) and movemnt horizontally are independet of each other. Lets think of something falling a free fall - a heavy ball say, from 64 m. We can calculate the time beacause we know how much 'g' is. (we can also measure the time). The independacy (or Superpostion) means that the time it will take the keys(or ball) to hit the ground is the same regardles of the horizontal velocity. It will always be the same (for this height) for anything or anybody that is falling a free fall! regardless of mass as well (that what Galileo Galilei proved in the pisa tower! remeber?). So now u just need to calculate the time of falling (like eSpex showed us). next in the x axis we have a constant velocity, thats nice, now x=vt. the distance will be the time time the velocity...
good luck!
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Answer 3

You are correct, guess that's what I get for not proof reading my answer. Thanks.

Answer 4

Ur wellcome happens to everyone.