Math Labs with Activity – To Prepare a Clinometer to Measure the Height of an Object
To prepare a clinometer and use it to measure the height of an object (say a lamp post)
- A thick chart paper
- A soft-drink straw
- A flexible string
- A small weight (a metal washer)
- A geometry box
Consider an object (e.g., a lamp post) at a distance d from you. Let your height be h1 and the height of the lamp post be h2. Let θ be the angle of elevation of the top of the lamp post with respect to your eye. If h = h2 – h1 then from Figure 42.1 we have h
tan θ = h/d, i.e., h = d tan 0.
height of the lamp post = h2 = h + h1= h1+ d tan θ.
Step 1: On the top side of the chart paper construct a large protractor as shown in Figure 42.2.
Step 2: Fix the soft-drink straw at the centre point O (as shown in Figure 42.2 using a nail. Ensure that the straw lies at your eye level.
Step 3: From the nail suspend a weight using a flexible string as shown in Figure 42.2.
Step 4: A clinometer (also called inclinometer, as it is used for measuring the angle of slope, elevation or inclination of an object) is thus prepared.
Step 5: Measure the distance d of the object (lamp post) from the clinometer.
Step 6: Look through the straw and keep on tilting it till you are able to see the top of the lamp post.
Step 7: Hold the clinometer in this position and record the angle of elevation of the top of the lamp post.
Step 8: Record your height also.
Observations and Calculations
Distance of the object from you = d.
Angle of elevation of the top of the lamp post with respect to your eye = θ.
Your height = h1.
Therefore, height of the lamp post h2=h1+d tan θ.