Physics

Physics

Problem

A stone is projected so that its maximum height above the point of projection is 5 m5\,\text{m}. The initial angle of projection is 30∘30^{\circ} and gg may be taken as 10 m s−210\,\text{m\,s}^{-2}. The initial speed of projection is a) 14 m s−114\,\text{m\,s}^{-1} b) 20 m s−120\,\text{m\,s}^{-1} c) 28 m s−128\,\text{m\,s}^{-1} d) 12 m s−112\,\text{m\,s}^{-1}
Intuitive explanation

The key is recognizing that at maximum height, all the vertical component of velocity becomes zero—so the stone's upward motion stops there. Use the kinematic relationship between initial vertical velocity, final vertical velocity (zero at the peak), and height to find the initial speed. Remember that only the vertical component of the initial velocity contributes to reaching maximum height, so you'll need to separate the initial speed into its sin⁡(30°)\sin(30°) component.

Intuitive explanation

The key is recognizing that at maximum height, all the vertical component of velocity becomes zero—so the stone's upward motion stops there. Use the kinematic relationship between initial vertical velocity, final vertical velocity (zero at the peak), and height to find the initial speed. Remember that only the vertical component of the initial velocity contributes to reaching maximum height, so you'll need to separate the initial speed into its sin⁡(30°)\sin(30°) component.

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