Answer :
Final answer:
The total time in the air for projectile motion is determined by the initial vertical velocity and the acceleration due to gravity. A projectile fired at an angle of 41.5 degrees with an initial speed of 37.9 m/s has an initial vertical velocity of approximately 25.21 m/s. Therefore the correct answer is None of the above.
Explanation:
In this case, the projectile is fired with an initial speed of 37.9 m/s at a 41.5-degree angle above the horizontal. The initial vertical velocity (vy) can be found using the sine function: vy = v * sin(θ), where v is the initial speed and θ is the launch angle.
The time the projectile spends in the air can then be determined by using the formula derived from the kinematic equations for uniformly accelerated motion (assuming downward acceleration due to gravity, g = 9.8 m/s2, and that the projectile lands at the same vertical level from which it was launched).
Applying this to the given situation:
Initial vertical velocity, vy = 37.9 m/s * sin(41.5°) = 37.9 * 0.6652 (using a calculator)
vy = 25.21 m/s (approximately)
Time to reach maximum height, tup = vy / g = 25.21 m/s / 9.8 m/s2
tup = 2.57 s (approximately)
Total time in the air = 2 * tup = 2 * 2.57 s = 5.14 s
