A ball whose kinetic energy is E, is projected at an angle of 45^∘ to the horizontal. The kineti

step 1 In this question we have given a ball whose kinetic energy is given to us that is E and it is pr

A ball whose kinetic energy is E, is projected at an angle...

A ball whose kinetic energy is $E$, is projected at an angle of $45^{\circ}$ to the horizontal. The kinetic energy of the ball at the highest point of its flight will be:
(a) $E$
(b) $\frac{E}{\sqrt{2}}$
(c) $\frac{E}{2}$
(d) Zero

Key Concepts

Energy Conservation in Projectile Motion

In projectile motion under the influence of gravity and absent external forces like air resistance, the total mechanical energy (kinetic plus potential) remains constant. At the highest point of the projectile's path, the vertical component of the velocity becomes zero, meaning all the kinetic energy is due to the horizontal component of the velocity.

Decomposition of Velocity

Decomposition of velocity involves breaking a velocity vector into its horizontal and vertical components, which is crucial in analyzing projectile motion. This separation allows one to determine how different components of motion (vertical and horizontal) contribute independently to the overall behavior of the projectile.

Projectile Motion

Projectile motion refers to the motion of an object that is launched into the air and is influenced only by gravity (neglecting air resistance). This type of motion is characterized by a parabolic trajectory, where the horizontal component of velocity remains constant while the vertical component changes due to gravitational acceleration.

Kinetic Energy

Kinetic energy is the energy that an object possesses due to its motion, mathematically expressed as one half times the mass times the square of the velocity. It is a scalar quantity that depends only on the speed of the object, regardless of the direction of motion.

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