Question

For a body projected at an angle with the horizontal from the ground, choose the correct statement.

• A. The Kinetic Energy (K.E.) is zero at the highest point of projectile motion.
• B. The horizontal component of velocity is zero at the highest point.
• C. The vertical component of momentum is maximum at the highest point.
• D. Gravitational potential energy is maximum at the highest point.

Hint:

In projectile motion, analyze the components of velocity and the energies (potential and kinetic) at different points of the trajectory, especially at the highest point.

Answer 1

The Correct Option is D

Step 1: Analyze the Projectile Motion at the Highest Point

When a body is projected at an angle with the horizontal, it follows a parabolic trajectory. At the highest point of its trajectory:

• The vertical component of velocity (\(v_y\)) is zero.
• The horizontal component of velocity (\(v_x\)) remains constant throughout the motion and is equal to \(u \cos \theta\), where \(u\) is the initial velocity and \(\theta\) is the angle of projection.

Step 2: Analyze the Gravitational Potential Energy

The gravitational potential energy (\(U\)) of a body at a height \(h\) above the ground is given by:

\[ U = mgh \]

where \(m\) is the mass of the body and \(g\) is the acceleration due to gravity. Since \(h\) is maximum at the highest point, the gravitational potential energy is also maximum at the highest point.

Step 3: Analyze the Horizontal Component of Velocity

The horizontal component of velocity remains constant throughout the projectile motion. It does not become zero at the highest point.

Step 4: Analyze the Vertical Component of Momentum

The vertical component of momentum is given by \(mv_y\). Since \(v_y = 0\) at the highest point, the vertical component of momentum is also zero at the highest point, not maximum.

Step 5: Analyze the Kinetic Energy

The kinetic energy (\(KE\)) of a body is given by:

\[ KE = \frac{1}{2} mv^2 \]

At the highest point, \(v_y = 0\), but \(v_x = u \cos \theta \neq 0\). Therefore, the total velocity \(v\) is not zero, and hence \(KE\) is not zero. The \(KE\) at the highest point is minimum but not zero.

Conclusion: Only statement (4) is correct. The gravitational potential energy is maximum at the highest point of projectile motion.

Answer 2

At highest point 
\(Vy​=0\) 
\(Vx​=ux​=ucosθ\) 
\(Ug​=mgh\), it is maximum at \(H_{max}\)​

The Correct Option is (D): Gravitational potential energy is maximum at the highest point.