Final answer:
To calculate the time of flight for a tennis ball projected at 3 m/s at a 30° angle, identify the initial vertical velocity and apply the formulas for projectile motion. The calculated time of flight is approximately 0.306 seconds.
Step-by-step explanation:
The question asks to calculate the time of flight of a tennis ball that is projected with an initial velocity of 3 m/s at an angle of 30° to the horizontal. To solve this, we need to use the equations of motion for projectile motion, focusing on the vertical component of the velocity, which is influenced by gravity (g = 9.8 m/s2).
The initial vertical velocity (Vy) can be calculated using the formula Vy = V * sin(θ), where V is the initial velocity and θ is the angle of projection. Hence, Vy = 3 m/s * sin(30°) = 1.5 m/s. The time of flight (T) is given by the formula T = 2 * Vy / g, as the ball has to go up and then come down back to the same level from which it was projected. So, T = 2 * 1.5 m/s / 9.8 m/s2 = 0.306 seconds (approximately). Therefore, the time of flight for the tennis ball is about 0.306 seconds.