Final answer:
Projectile motion involves calculating the time of flight, range, and maximum height of a projectile using its initial velocity and angle of projection, with the horizontal range and time affected by horizontal and vertical velocity components.
Step-by-step explanation:
The question is related to the topic of projectile motion in physics and deals with a projectile launched from the ground level at an initial velocity of 40 m/s at an angle where tan θ = 3. To calculate the time of flight, time taken to reach the maximum height, and the maximum height, one would use the equations of motion for projectiles.
The initial speed can be broken into horizontal (vx) and vertical (vy) components using the given angle of projection (θ). The maximum height (H) can be determined using the vertical component of velocity and the acceleration due to gravity (g).
The time of flight (T) would be the total time the projectile spent in the air until it returns to the ground level. It is calculated by 2vy/g because the projectile takes the same amount of time to reach the maximum height as it does to descend from it. The horizontal range (R) is the horizontal distance traveled by the projectile, calculated by vx * T.