Question

A soccer ball, at rest on the ground, is kicked with an initial velocity of 10 m/s at a launch angle of 30°. Calculate its total flight time, assuming that air resistance is negligible.

(A) 0.5 s

(B) 1 s

(C) 2 s

(D) 4 s

Answer 1

The total flight time of the soccer ball is calculated using the vertical component of the initial velocity, and considering the influence of gravity. The correct flight time is approximately 1.02 seconds, which matches closest to option (B) 1 s.

Step-by-step explanation:

The student is asking to calculate the total flight time of a soccer ball that is kicked with an initial velocity of 10 m/s at an angle of 30°, under the assumption that air resistance is negligible. To calculate the total flight time, we need to consider only the vertical component of the initial velocity because horizontal motion does not affect the time the ball is in the air. The vertical component (Vyi) can be found by using the sine function of the angle times the initial velocity:

Vyi = V * sin(θ)

Vyi = 10 m/s * sin(30°) = 10 m/s * 0.5 = 5 m/s

Using the vertical component, we calculate the time it takes for the ball to reach the peak of its trajectory, which is the time it takes for gravity to decelerate the ball to a stop:

t = Vyi / g

Where g is the acceleration due to gravity (approximately 9.81 m/s²). The total flight time is twice this because the ball takes the same amount of time to descend as it does to rise:

t = (2 * Vyi) / g = (2 * 5 m/s) / 9.81 m/s² ≈ 1.02 s

Thus, the closest answer from the given options is (B) 1 s.