Problem

Problem

A body is projected at time t=0t = 0 from a certain point on a planet's surface with a certain velocity at a certain angle with the planet's surface (assumed horizontal). The horizontal and vertical displacements xx and yy (in metre) respectively vary with time tt in second as, x=(103)tx = (10\sqrt{3})t and y=10t−t2y = 10t - t^2 . The maximum height attained by the body is a. 75 m b. 100 m c. 50 m d. 25 m
Intuitive explanation

This is a projectile motion problem where you're given the position equations directly rather than initial conditions. The key insight is that maximum height occurs when the vertical velocity becomes zero—that's when the body stops rising and is about to fall. Find when dydt=0\frac{dy}{dt} = 0, then substitute that time back into the y(t)y(t) equation to get the maximum height. The equations already encode all the physics; you just need to extract the turning point.

Intuitive explanation

This is a projectile motion problem where you're given the position equations directly rather than initial conditions. The key insight is that maximum height occurs when the vertical velocity becomes zero—that's when the body stops rising and is about to fall. Find when dydt=0\frac{dy}{dt} = 0, then substitute that time back into the y(t)y(t) equation to get the maximum height. The equations already encode all the physics; you just need to extract the turning point.

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