Q2DQ - University Physics with Modern Physics

Question

A projectile has the same initial kinetic energy no matter what the angle of projection. Why doesn’t it rise to the same maximum height in each case?

Step-by-Step Solution

Answer

The projectiles do not lose the same amount of kinetic energy that’s why they do not rise to the same maximum height.

Step 1: Concept/Significance of maximum height of the projectile

The maximum height of the projectile is given by,

 $\mathit{h}\mathbf{=}\frac{{\mathbf{v}}_{\mathbf{0}}\mathbf{s}\mathbf{i}{\mathbf{n}}^{\mathbf{2}}\mathbf{\theta }}{\mathbf{2}\mathbf{g}}$

Here, g is the acceleration due to gravity, ${\mathit{v}}_{\mathbf{0}}$ is the initial velocity, and the angle of the projectile.

Step 2: Explain the reason why the projectile does not rise to the same maximum height in each case

The conservation of energy states that the gain in the potential energy is equal to the loss in kinetic energy.

 $∆KE=mgh$

The maximum height is dependent on $\theta$ , whereas the initial kinetic energy is independent of $\theta$ .

 

The greater the loss of kinetic energy, the greater will be the height of the projectile. Even though the initial kinetic energy of the particle is the same, they do not reach the maximum height because they do not lose the same amount of kinetic energy.

 

Therefore, the projectiles do not rise to the same maximum height because projectiles do not lose the same amount of kinetic energy.