Math Labs with Activity – To Prepare a Clinometer to Measure the Height of an Object

Math Labs with Activity – To Prepare a Clinometer to Measure the Height of an Object

OBJECTIVE

To prepare a clinometer and use it to measure the height of an object (say a lamp post)

Materials Required

1. A thick chart paper
2. A soft-drink straw
3. A flexible string
4. A small weight (a metal washer)
5. A geometry box

Theory
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.

Procedure
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.

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