Final answer:
The initial horizontal velocity is 30 m/s, the initial vertical velocity is 14.3 m/s, and the total time the arrow is in the air is 2.0 seconds.
Step-by-step explanation:
To solve this problem, we can use the equations of projectile motion. Let's break down each part:
a) Initial Horizontal Velocity:
The horizontal velocity remains constant throughout the motion. Since there are no horizontal forces acting on the arrow, the initial horizontal velocity is the same as the final horizontal velocity. Therefore, the initial horizontal velocity is 30 m/s.
b) Initial Vertical Velocity:
The vertical velocity changes due to the acceleration of gravity. To find the initial vertical velocity, we can use the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. In this case, the final velocity is 0 at the highest point of the trajectory, so we can rearrange the equation to solve for the initial vertical velocity. By substituting the values we have, the initial vertical velocity is 14.3 m/s.
c) Total Time in the Air:
The total time in the air can be found using the equation t = 2 * u * sin(theta) / g, where u is the initial velocity, theta is the launch angle, and g is the acceleration due to gravity. By substituting the given values, the total time the arrow is in the air is 2.0 seconds.