Problem:

A spelunker finds a keep hole in a cave. She drops a pebble into the hole and hears a splash two secs later. She remembers that the acc. due to gravity is about 10 m/s, and that sound travels at 300 m/s. From this, she determines the depth of the hole, taking into account that it takes time for the sound to reach her. How deep is the hole?

Answer:

Using the equation delta x = Vi deltaT + 1/2 a delta T squared, I came up with 20 meters for the depth of the whole, which made me feel pretty stupid as I could have deduced that just from seeing that it took a pebble two secs to make a sound at 10 m/s. However, I know that the sound and the time it takes to reach her ears must be accounted for as well, and I dont know how. I know any amount of time I get from the sound is going to be very tiny since it goes so fast, but I cant shake the feeling that i'm missing something. Anyone?

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Problem:

A person sees a flowerpot falling past a window. The window is 1.5 m high, and it takes 0.3 secs for the pot to fall past the window.

--Find speed that the flowerpot had when it was on top of the window.

--Using result, find height from which the pot fell, assuming it fell from rest.

Answers:

For the first part, I got 4.9 m/s for the speed. For the second, I got that it fell from 1.91 meters. Right? Wrong? Horribly wrong?

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Problem:

A car is at a constant speed of 55 m/s. It passes a motorcycle at rest by the side of the road. Just as the car passes, the cycle begins to accelerate with constant acceleration of 3.5 m/s.

--Write an equation for the position of the car as a function of time. Write another equation for the position of the cycle as a function of time. Now write an equation that expresses the condition that the cyle caught up with the car. Use this to find the time that they cycle needs to catch the car.

Answer:

I actually just dont know where to start on this one. I dont know if I should make the equation start with delta T, or delta X, or whatever. Any help would be appreciated, and thanks in advance.