To find the time of flight of a projectile, we can analyze the motion in the horizontal and vertical directions separately.
Given: Initial velocity (Vi) = 30 m/s Launch angle (θ) = 75 degrees
First, we can calculate the time it takes for the projectile to reach the highest point of its trajectory. At the highest point, the vertical velocity component becomes zero.
Vertical velocity (Vy) = Vi * sin(θ)
Since the time taken to reach the highest point is the same as the time taken to descend from the highest point to the ground, we can use the vertical motion equation to find the time of ascent (t1) and the time of descent (t2).
t1 = t2 = Vy / g
where g is the acceleration due to gravity (approximately 9.8 m/s²).
Next, we can calculate the total time of flight (t) by adding the time of ascent and the time of descent.
t = t1 + t2
To find t1 and t2, we need to calculate Vy.
Vy = Vi * sin(θ) = 30 m/s * sin(75°)
Now we can calculate Vy:
Vy = 30 m/s * sin(75°) ≈ 30 m/s * 0.966 ≈ 28.98 m/s
Now we can calculate t1 and t2:
t1 = t2 = Vy / g = 28.98 m/s / 9.8 m/s² ≈ 2.96 s
Finally, we can find the total time of flight:
t = t1 + t2 = 2.96 s + 2.96 s ≈ 5.92 s
Therefore, the time of flight of the sipak takraw ball is approximately 5.92 seconds.