Question

Lionel Messi kicks a ball at an initial velocity of 27 m/s at an angle of 40 degrees above the horizontal. How long does it take for the ball to land?

A) 1.5 seconds
B) 3.03 seconds
C) 5.0 seconds
D) 10.0 seconds

Answer 1

The time it takes for the ball to land after being kicked by Lionel Messi, with an initial velocity of 27 m/s at a 40-degree angle, is approximately 3.03 seconds.

Step-by-step explanation:

To find out how long it takes for the ball to land, we analyze the vertical motion of the ball separately from the horizontal motion, since the two are independent in projectile motion. Given the initial velocity of 27 m/s at a 40-degree angle, we first need to find the vertical component of the initial velocity. The vertical component (Vy) can be found using trigonometry: Vy = Vsin(θ) = 27 m/s * sin(40 degrees).

Using the formula for time of flight in projectile motion, which is T = (2 * Vy) / g, where g is the acceleration due to gravity (approximately 9.81 m/s2), we can calculate the total time the ball is in the air. Plugging in the numbers, we get T = (2 * 27 * sin(40)) / 9.81.

After solving, the time of flight or the total time the ball remains in the air comes out close to option B) 3.03 seconds, which means that would be the correct choice as to how long it takes for the ball to land.