In a circus act, a 60 kg clown is shot from a cannon with an initial velocity of 16 m / s at s

step 1 Mass of the clown m is equal to 60 kilograms. M is equal to 60 kilograms and initial velocity VI

In a circus act, a 60 kg clown is shot from a cannon with...

In a circus act, a $60 \mathrm{~kg}$ clown is shot from a cannon with an initial velocity of $16 \mathrm{~m} / \mathrm{s}$ at some unknown angle above the horizontal. A short time later the clown lands in a net that is $3.9 \mathrm{~m}$ vertically above the clown's initial position. Disregard air drag. What is the kinetic energy of the clown as he lands in the net?

Key Concepts

Projectile Motion

Projectile motion describes the trajectory of an object that is launched into the air and is subject only to gravitational acceleration (when air resistance is neglected). This concept involves analyzing the motion in both horizontal and vertical directions, which is essential in decomposing the initial velocity and understanding the energy transitions during the flight.

Gravitational Potential Energy

Gravitational potential energy is the energy stored in an object due to its position in a gravitational field, often expressed as mgh, where h is the height above a reference point. This concept is key to understanding how an object’s energy is partitioned when it is elevated, as seen with the clown landing higher than his launch point.

Conservation of Mechanical Energy

This concept states that in the absence of non-conservative forces (like air resistance), the total mechanical energy of a system (the sum of kinetic and potential energies) remains constant. In scenarios involving projectiles, it allows us to relate the kinetic energy at launch and the kinetic energy at a different height by accounting for the change in gravitational potential energy.

Kinetic Energy

Kinetic energy is the energy possessed by an object due to its motion, typically calculated using the formula ½mv². In this problem, determining the kinetic energy when the clown reaches a net involves understanding how the initial kinetic energy is reduced by the gain in gravitational potential energy as the clown ascends.

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