Question

A cannon fires a cannon ball with an initial velocity of 100 m/s, but instead of being completely horizontal, the velocity is directed at 30° above the horizontal. The ball lands at the same height from which it was fired. What is the initial velocity in the x-direction?

Answer 1

The initial velocity in the x-direction of the cannon ball fired at 30° above the horizontal with an initial speed of 100 m/s is approximately 86.6 m/s, calculated using the cosine of the launch angle multiplied by the initial speed.

Step-by-step explanation:

The question is asking for the initial velocity in the x-direction (horizontal component) of a cannon ball fired at an angle of 30° above the horizontal. The initial velocity of the cannon ball is given as 100 m/s. To find the initial velocity in the x-direction, we use the cosine function since the x-component is adjacent to the angle of launch.

The initial velocity in the x-direction (Vx) is calculated using the following formula:

Vx = V * cos(θ)

Where V is the total initial velocity and θ is the angle of launch.

The calculation is as follows:

Vx = 100 m/s * cos(30°) ≈ 100 m/s * 0.866 ≈ 86.6 m/s

Therefore, the initial velocity in the x-direction is approximately 86.6 m/s.