In this lab, you will be asked to calculate the height of some objects outside using two methods. Your final product will be your calculations and results as well as the answers to the questions.

You know now that objects near the surface of the Earth fall at an acceleration of about 10 m/s/s. We will use this fact to estimate the height of tall objects.

- A lamp post in the parking lot
- One of the trees in front of the school
- Another tall object of your choice

- stopwatch
- lab notebook
- calculator
- ball (ex, a golf ball)

If you time how long it takes for an object to fall from the height of one of the items above you can easily estimate the height using the formula d = ½gt^{2}. Here g = 10 m/s/s, t is the time in s, and d is the distance. Note that the time in this formula is just the time for an object to fall. So if you time how long it takes to go from your hand to the top of the object and back to your hand, you should divide the time you find in half. Also, it is important to add in the height of your hand since the formula only knows about the time the object fell and it didn’t fall onto the ground (if you caught it!).

Another way to use the time for an ball to fall to find height is to throw the ball higher than the lampost (for example) and time the fall from when it goes past the top to when it hits the ground. Then just put the time found into the formula.

Another way to estimate height is to measure someone in your lab group and have them stand right at the base of the object to be measured. If another person stand sufficiently far away they can exactly cover the person up with their hand. By counting how many ‘hand heights’ it takes to get to the top of the object it is possible to figure out how tall the object is. Just multiply how many ‘person heights’ you find by the person’s height. This second method for measuring height you will take as the *accepted value* of the height.

- What is your percent error for each object?

| accepted value – experimental value | % error = ———————————————————————————————————————— × 100% accepted value

- Which method do you think worked best? (The hand-height method or the freefall method) Why?
- Does the freefall method work better on high objects or low objects? Explain.
- How could you improve the freefall method of estimating height? (The one where you use a ball and a stopwatch).

- The heights of each of the three objects you measured should be reported in a neat table. Report the height found using both methods and the percent error for each object.
- Show how you calculated the height from the falling ball only once. Show how you calculated height using your second method (either hand-heights or similar triangles or trigonometry) also only once. Make these calculations neat and easy to read and show all steps. Include units at each step of the calculation.
- After these items, answer the questions above.

- Calculate the heights using similar triangles (geometry) or using trignometry and use this as your accepted value or…
- Show how the formula d = ½gt
^{2}can be found from our table of distances fallen, times, and velocities, or… - ???