The equation of trajectory ofa projectile is `y = 10x-5/9x^2` If we assume `g = 10 ms^(-2)`, the range of projectile (in metre) is

Options

A. 36
B. 24
C. 18
D. 9

Answer

To find the range of the projectile given the equation of its trajectory \( y = 10x - \frac{5}{9}x^2 \), we can follow these steps:

### Step 1: Set the equation of trajectory to zero
To find the range, we need to determine the points where the projectile hits the ground. This occurs when \( y = 0 \). Therefore, we set the equation to zero:

\[ 0 = 10x - \frac{5}{9}x^2 \]

### Step 2: Factor the equation
We can factor out \( x \) from the equation:

\[ x(10 - \frac{5}{9}x) = 0 \]

### Step 3: Solve for \( x \)
This gives us two solutions:

1. \( x = 0 \) (the starting point)
2. \( 10 - \frac{5}{9}x = 0 \)

Now, we solve the second equation for \( x \):

\[ 10 = \frac{5}{9}x \]

Multiplying both sides by \( 9 \):

\[ 90 = 5x \]

Now, divide both sides by \( 5 \):

\[ x = 18 \]

### Step 4: Conclusion
The range of the projectile is the value of \( x \) when it hits the ground, which we found to be:

\[ \text{Range} = 18 \text{ meters} \]

Thus, the range of the projectile is **18 meters**.

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