If a ball is thrown straight upward with an initial velocity...

If a ball is thrown straight upward with an initial velocity of $v,$ it will reach a
height of $h .$ If the initial speed of the ball is doubled, what will be the new
maximum height?
(A) $\sqrt{2}(h)$
(B) 2$h$
(C) 2$\sqrt{2}(h)$
(C) 2$\sqrt{2}(h)$
(D) 4$h$
(E) 4$\sqrt{2}(h)$

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Key Concepts

Projectile Motion

Projectile motion involves analyzing objects launched into the air subject only to gravitational acceleration. It focuses on how an initial velocity, when acting against gravity, determines the trajectory and maximum height of the object, using kinematic equations to describe the motion.

Conservation of Energy

In vertical projectile motion, the principle of conservation of energy is often used to relate the initial kinetic energy of the projectile to its gravitational potential energy at the maximum height. This approach helps establish that maximum height is proportional to the square of the initial speed.

Scaling Relationships

Scaling relationships in physics reveal how changes in one quantity affect another. In this context, since kinetic energy varies as the square of the velocity, doubling the initial speed results in a quadrupling of the kinetic energy, which in turn quadruples the maximum height reached.

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