A pendulum of length 11 . cm is swinging from a fixed point , as shown. Calculate the distance that the end of the pendulum travels when it swings through an angle of 84^circ Give your answer in centimetres (cm) to 1 d.p.

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A pendulum of length 11 . cm is swinging from a fixed point , as shown. Calculate the distance that the end of the pendulum travels when it swings through an angle of 84^circ Give your answer in centimetres (cm) to 1 d.p.

Answer 1

### Step 1: Theta in Radians = \( 84^{\circ} \) * \( \frac{\pi}{180} \) = 1.47 rad ### Step 2: Substituting: s = 11 cm * 1.47 rad ### Step 3: Calculating for s (distance that the end of the pendulum travels): s = 11 cm * 1.47 rad = 16.2 cm

Answer 2

## Step 1: The first step to solve this problem is to convert the angle from degrees to radians. The conversion rate from degrees to radians is that \( \pi \) radians equals \( 180^{\circ} \). Thus, by ratio, we have \( \Theta \) rad = \( \Theta^{\circ} \) * \( \frac{\pi}{180} \). ## Step 2: The second step is to use the formula that relates the arc length (s), the radius (r - which is the length of the pendulum), and the swept angle (θ radians) of a circle, which is \( s = r * \theta \). In this specific case of the question, we have the length of the pendulum (r = 11 cm) and the swept angle (Θ = 84°), while we are asked to find the arc length (s - the distance that the end of the pendulum travels). ## Step 3: Substitute the values into the formula \( s = r * \theta \) to derive the required distance that the end of the pendulum travels (s).

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A pendulum of length 11 . cm is swinging from a fixed point , as shown. Calculate the distance that the end of the pendulum travels when it swings through an angle of 84^circ Give your answer in centimetres (cm) to 1 d.p.

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