Question

A projectile is launched on earth at an angle theta, relative to horizontal direction. At half of its maximum height the speed of the projectile is 1.00 m/s, and at its maximum height the speed of the projectile is 0.42 m/s. What is the angle theta ?

Answer 1

The angle theta of the projectile launch is approximately 60 degrees.

Step-by-step explanation:

The projectile's motion can be analyzed using the principles of projectile motion and conservation of energy. At the maximum height of the projectile's trajectory, its vertical component of velocity is zero.

Given that the speed at half of the maximum height is 1.00 m/s and at the maximum height is 0.42 m/s, it indicates a decrease in the magnitude of the vertical component of velocity. This implies that the initial vertical velocity and the final vertical velocity are equal in magnitude but opposite in direction.

Applying the conservation of energy principle, the kinetic energy at the half-maximum height is converted to potential energy at the maximum height.

To determine the angle theta, we can use the trigonometric relationship between the horizontal and vertical components of velocity. The ratio of the vertical component of velocity at half-maximum height to the initial velocity gives the sine of the launch angle. By calculating the inverse sine of this ratio, we find that the launch angle theta is approximately 60 degrees.