Three construction workers can throw bricks vertically up...

Three construction workers can throw bricks vertically up with speeds of $4 \mathrm{~m} \mathrm{~s}^{-1}, 6 \mathrm{~m} \mathrm{~s}^{-1}$ and $12 \mathrm{~m} \mathrm{~s}^{-1}$ respectively. Working together, they can stack them on a platform of maximum height (in $\mathrm{m}$ ) (a) 5 (b) 10 (c) 15 (d) 20

Key Concepts

Projectile Motion

Projectile motion describes the behavior of an object projected into the air, subject only to gravity. It covers the motion’s vertical component, where the initial speed, gravitational acceleration, and the resulting maximum height are related by the equation h = v²/(2g). This relation directly underpins the determination of how high an object can be thrown when only gravity acts on it.

Energy Conservation in Motion

The principle of energy conservation is fundamental in analyzing projectile motion. A projectile’s initial kinetic energy, when thrown upwards, is progressively converted into gravitational potential energy until it comes momentarily to rest at its maximum height. This conversion explains the relationship between the speed of projection and the height reached, and it is key in solving problems involving vertical throwing.

Sequential Task Optimization in Stacking

When multiple actions contribute to a cumulative goal, such as stacking objects or sequentially building a structure, the order in which resources are used is crucial. In such scenarios, the contributions must be arranged to maximize the overall outcome, which means that the parts with lower individual limits are used as the base and supplemented by actions with higher capabilities. This sequential optimization ensures that each element’s maximum potential is fully utilized in the cumulative process.

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