The kinetic energy (KE) of an object is given by the formula KE = 1/2 mv², where m is the mass of the object and v is its velocity. When the ball is projected at an angle, its velocity has two components: a horizontal component (v cos θ) and a vertical component (v sin θ).

At the highest point of its flight, the vertical component of the velocity becomes zero because the ball is momentarily at rest at this point. However, the horizontal component of the velocity remains unchanged throughout the flight because there are no horizontal forces acting on the ball (assuming air resistance is negligible).

Therefore, at the highest point of the flight, the velocity of the ball is equal to the horizontal component of the initial velocity, which is v cos θ.

Substituting this into the formula for kinetic energy, we get KE = 1/2 m (v cos θ)².

Since the kinetic energy at the highest point is less than the initial kinetic energy (because v cos θ

Question

The kinetic energy (KE) of an object is given by the formula KE = 1/2 mv², where m is the mass of the object and v is its velocity. When the ball is projected at an angle, its velocity has two components: a horizontal component (v cos θ) and a vertical component (v sin θ).

At the highest point of its flight, the vertical component of the velocity becomes zero because the ball is momentarily at rest at this point. However, the horizontal component of the velocity remains unchanged throughout the flight because there are no horizontal forces acting on the ball (assuming air resistance is negligible).

Therefore, at the highest point of the flight, the velocity of the ball is equal to the horizontal component of the initial velocity, which is v cos θ.

Substituting this into the formula for kinetic energy, we get KE = 1/2 m (v cos θ)².

Since the kinetic energy at the highest point is less than the initial kinetic energy (because v cos θ < v), the kinetic energy at the highest point is less than E.

So, the kinetic energy of the ball at the highest point of its flight will be 1/2 m (v cos 60°)² = 1/2 m (v/2)² = E/4 (assuming the initial kinetic energy E = 1/2 mv²).

Knowee AI · Accepted Answer

The kinetic energy (KE) of an object is given by the formula KE = 1/2 mv², where m is the mass of the object and v is its velocity. When the ball is projected at an angle, its velocity has two components: a horizontal component (v cos θ) and a vertical component (v sin θ).

At the highest point of its flight, the vertical component of the velocity becomes zero because the ball is momentarily at rest at this point. However, the horizontal component of the velocity remains unchanged throughout the flight because there are no horizontal forces acting on the ball (assuming air resistance is negligible).

Therefore, at the highest point of the flight, the velocity of the ball is equal to the horizontal component of the initial velocity, which is v cos θ.

Substituting this into the formula for kinetic energy, we get KE = 1/2 m (v cos θ)².

Since the kinetic energy at the highest point is less than the initial kinetic energy (because v cos θ < v), the kinetic energy at the highest point is less than E.

So, the kinetic energy of the ball at the highest point of its flight will be 1/2 m (v cos 60°)² = 1/2 m (v/2)² = E/4 (assuming the initial kinetic energy E = 1/2 mv²).

A ball is projected with kinetic energy E, at an angle of 60° to the horizontal. The kinetic energy of this ball at the highest point of its flight will become:

Question

Solution

Similar Questions

Upgrade your grade with Knowee