Answer to Question #143105 in Physics for serrene

Question

Is the angle of projection really affects the height of the trajectory and its horizontal
range? Explain.

Answer 1

Yes, the range and height of a trajectory really depend on the angle above the horizontal at which a body was launched. Look at the equations for height and range:

$$h(\theta)=\frac{(v\text{ sin}\theta)^2}{2g},\\\space\\ R(\theta)=\frac{v^2\text{ sin}(2\theta)}{g}.$$

As we see, the maximum height is at 90°-angle to the ground:

$$h(90°)=\frac{v^2}{2g}.$$

The range, however, is zero at this angle. But the maximum range is at 45°:

$$R(45°)=\frac{v^2}{g}.$$