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A cricketer hits a ball in a vertical x-...

A cricketer hits a ball in a vertical x-y plane from the ground level with a velocity `barV_0=(10sqrt(3i)+30hatj)` m/s.Find the time in which velocity vector makes an angle of `30 ^(@)` with horizontal x- axis (g=10 `m//s^(2))`

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To solve the problem, we need to find the time \( t \) when the velocity vector of the ball makes an angle of \( 30^\circ \) with the horizontal x-axis. The initial velocity vector is given as \( \bar{V_0} = (10\sqrt{3} \hat{i} + 30 \hat{j}) \) m/s, and the acceleration due to gravity \( g = 10 \, \text{m/s}^2 \). ### Step-by-step Solution: 1. **Identify the Components of Initial Velocity:** The initial velocity \( \bar{V_0} \) can be broken down into its components: - \( V_{0x} = 10\sqrt{3} \, \text{m/s} \) (horizontal component) - \( V_{0y} = 30 \, \text{m/s} \) (vertical component) ...
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