If a projectile has maximum range of 36m, find the speed of projection (Take g = 9.8m/s2)

1. Analyze the Question

We are given the maximum range ($R_{max}$) of a projectile as 36m and the acceleration due to gravity ($g$) as $9.8 \, \text{m/s}^2$. We need to calculate the initial speed of projection ($u$).

2. Explain the Concept

The range of a projectile is given by the formula:

For a projectile to achieve its maximum range, the angle of projection ($\theta$) must be $45^\circ$. Since $\sin(2 \times 45^\circ) = \sin(90^\circ) = 1$, the formula for maximum range simplifies to:

3. Show the Solution

• Step 1: State the formula for maximum range. $$R_{max} = \frac{u^2}{g}$$

• Step 2: Substitute the given values into the formula. $$36 = \frac{u^2}{9.8}$$

• Step 3: Solve for $u^2$. $$u^2 = 36 \times 9.8$$ $$u^2 = 352.8$$

• Step 4: Find the square root to get $u$. $$u = \sqrt{352.8}$$ $$u \approx 18.78 \, \text{m/s}$$

Rounding this value to the nearest whole number gives us 19 m/s.

4. Identify the Answer

Comparing our result ($18.78 \, \text{m/s}$) to the provided options, it aligns with option A.

Note: Options C and D are incorrect because they provide units for acceleration ($\text{m/s}^2$) rather than speed ($\text{m/s}$).

5. Exam Tip

Always check the units in your options! If a question asks for "speed," the answer must be in $\text{m/s}$. If you see options with $\text{m/s}^2$, you can immediately eliminate them as they represent acceleration, not speed. This is a quick way to narrow down your choices in JAMB.