A stone is thrown vertically upwards. When the stone is at a height equal to half of its maximum height its speed will be 10 m/s, then the maximum height attained by the stone is (Take g = 10 m/$s^2$)
A. 3 m
B. 15 m
C. 1 m
D. 10 m

Hint: The maximum height of an object in a projectile trajectory happens when the vertical segment of velocity rises to zero. As the projectile moves upwards it conflicts with gravity, and in this manner the velocity starts to decelerate.

Complete step-by-step answer:
Inevitably the vertical velocity will arrive at zero, and the projectile is quickened descending under gravity right away. When the projectile arrives at its greatest tallness, it starts to quicken descending. This is likewise where you would draw a vertical line of balance.
The correct answer is D.
\[v_{1}^{2}={{u}^{2}}-2gh,\]
\[{{(10)}^{2}}={{u}^{2}}-2\times 10\times \dfrac{h}{2}\]
\[100={{u}^{2}}-10h\]
\[v_{2}^{2}={{u}^{2}}-2gh\]
\[{{(0)}^{2}}={{u}^{2}}-2\times 10\times h\]
\[{{u}^{2}}=20h~~\]
\[100=10h\]
\[h=10m\]
The main force of essentialness that follows up on the object is gravity, which acts descending, along these lines conferring to the object a descending speed up. Due to the object's latency, no outside flat force is expected to keep up the level velocity segment of the object. Considering different forces, for example, erosion from streamlined drag or inward drive, like, in a rocket, requires extra examination.

A ballistic rocket is a rocket just guided during the moderately short starting powered period of flight, and whose ensuing course is administered by the laws of old-style mechanics.

Ballistics ("to toss") is the study of mechanics that manages the flight, conduct, and impacts of projectiles, particularly shots, unguided bombs, rockets, or something like that; the science or craft of structuring and quickening projectiles in order to accomplish an ideal exhibition.

Note: In projectile motion, horizontal motion and the vertical motion are free of one another; that is, neither one of the motions influences the other. This is the guideline of compound motion set up and utilized by him to demonstrate the explanatory type of projectile motion. The horizontal and vertical segments of a projectile's velocity are autonomous of one another.