Final answer:
To find the velocity and position of the cannonball as a function of time, break the motion into horizontal and vertical components. Calculate the initial horizontal and vertical velocities using the given initial speed and launch angle. Express the position of the cannonball at any time t in vector form.
Step-by-step explanation:
To find the velocity and position of the cannonball as a function of time, we need to break the motion into horizontal and vertical components. The initial velocity can be decomposed into its x and y components using trigonometry. The horizontal velocity remains constant throughout the motion, while the vertical velocity changes over time due to the acceleration due to gravity.
Using the given initial speed of 50 m/s and the launch angle of 30°, we can calculate the initial horizontal velocity (Vx) and initial vertical velocity (Vy). The horizontal velocity (Vx) is given by Vx = initial speed * cos launch angle, and the vertical velocity (Vy) is given by Vy = initial speed * sin launch angle.
The position of the cannonball at any time t can be expressed in vector form, with the x-coordinate given by x = initial horizontal velocity * t and the y-coordinate given by y = initial vertical velocity * t - 0.5 * acceleration due to gravity * t^2, where the acceleration due to gravity is the negative value of the constant g m/s².