A stone thrown vertically upwards with a speed of 5 m s^-1 attains a height of h1. Another sto

step 1 As we know that the maximum height reached by any particle from vertically upward is equals to H

A stone thrown vertically upwards with a speed of 5 m s^-1...

A stone thrown vertically upwards with a speed of $5 \mathrm{~m} \mathrm{~s}^{-1}$ attains a height of $\mathrm{h}_{1}$. Another stone thrown vertically upwards from the same point with a velocity $10 \mathrm{~m} \mathrm{~s}^{-1}$ attains a height of $\mathrm{h}_{2}$. The relation between $\mathrm{h}_{1}$ and $\mathrm{h}_{2}$ is (a) $\mathrm{h}_{1}=\mathrm{h}_{2} / 2$ (b) $\mathrm{h}_{2}=2 \mathrm{~h}_{1}$ (c) $\mathrm{h}_{1}=3 \mathrm{~h}_{2}$ (d) $\mathrm{h}_{2}=4 \mathrm{~h}_{1}$

A stone thrown vertically upwards with a speed of $5 \mathrm{~m} \mathrm{~s}^{-1}$ attains a height of $\mathrm{h}_{1}$. Another stone thrown vertically upwards from the same point with a velocity $10 \mathrm{~m} \mathrm{~s}^{-1}$ attains a height of $\mathrm{h}_{2}$. The relation between $\mathrm{h}_{1}$ and $\mathrm{h}_{2}$ is
(a) $\mathrm{h}_{1}=\mathrm{h}_{2} / 2$
(b) $\mathrm{h}_{2}=2 \mathrm{~h}_{1}$
(c) $\mathrm{h}_{1}=3 \mathrm{~h}_{2}$
(d) $\mathrm{h}_{2}=4 \mathrm{~h}_{1}$

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Key Concepts

Uniform Acceleration

Uniform acceleration is the concept where an object's acceleration remains constant throughout its motion. When analyzing objects under the influence of gravity, it simplifies the computation of quantities like displacement, velocity, and time since gravitational acceleration (g) is taken as a constant value near Earth's surface.

Maximum Height in Projectile Motion

The maximum height reached by an object thrown vertically upward can be derived from the equation h = v²/(2g), which shows that the height is directly proportional to the square of the initial velocity and inversely proportional to the gravitational acceleration. This principle is used to compare different throws.

Quadratic Dependence on Initial Velocity

In projectile motion, the maximum height is proportional to the square of the initial velocity. This means that if the initial velocity is increased by a factor, the height increases by the square of that factor. For example, doubling the velocity increases the height by a factor of four, illustrating the quadratic relationship.

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