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A projectile is thrown with an initial v...

A projectile is thrown with an initial velocity of `v = a hat i + b hat j`. If the range of projectile is double the maximum height reached by it. Find the ratio `(b)/(a)`.

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To solve the problem, we need to analyze the motion of a projectile thrown with an initial velocity expressed in vector form as \( \mathbf{u} = a \hat{i} + b \hat{j} \). We are given that the range \( R \) of the projectile is double the maximum height \( H \) reached by it. We need to find the ratio \( \frac{b}{a} \). ### Step-by-Step Solution: 1. **Identify the Components of Initial Velocity**: The initial velocity \( \mathbf{u} \) can be broken down into its horizontal and vertical components: - Horizontal component: \( u_x = a \) - Vertical component: \( u_y = b \) ...
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