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class9 math ex6.2 q6 federal board

Class9 math ex6.2 q6 federal board will be solved.

A motorcycle is travelling on a curve along a highway. The curve is an arc of circle with radius of 10 km. If the motorcycle’s speed is 42 km/h. What is the angle is degree through which the motorcycle will turn in 21 minutes?

Math Class 9 New Book – Exercise 6.2, Question 6 (Federal Board)

This problem is taken from the Class 9 Mathematics New Book, Exercise 6.2, Question 6, under the Federal Board curriculum. It focuses on understanding circular motion and trigonometric applications.

Step 1: Understanding the Motion

When a vehicle moves along a circular path, the angle it turns through is directly related to the distance it travels along the curve. The relationship is given by:

$\theta = \frac{s}{r}$ $\theta$ $s$ $r$

Step 2: Calculate the Distance Travelled

Speed = 42 km/h
Time = 21 minutes (convert to hours: $21 / 60 = 0.35 hours$

$The distance travelled is:$

s=Speed × Times=42×0.35=14.7 km

Step 3: Find the Angle in Radians

Using the formula:

$\theta = \frac{14.7}{10} = 1.47 \text{ radians}$

step 4: Convert Radians to Degrees

$1$

radian = 57.3 degrees, we convert:

$\theta = 1.47 \times 57.3$ $\theta \approx 84.2^{\circ}$

Conclusion:-

In 21 minutes, the motorcycle will turn approximately 84.2 degrees while following the curved road. This calculation is useful in real-world applications such as road design, racing, and understanding the dynamics of vehicle movement on curves.