Final answer:
The ball kicked at an angle of 62 degrees with an initial speed of 18 m/s will be in the air for approximately 3.24 seconds after calculating the initial vertical velocity and using the time of flight formula for projectile motion.
Step-by-step explanation:
To calculate how long the ball is in the air, we need to consider the vertical motion of the ball, governed by the equation for the time of flight in projectile motion: t = (2 * v * sin(θ)) / g, where v is the initial velocity, θ is the launch angle, and g is the acceleration due to gravity (9.8 m/s²). Given the initial velocity of 18 m/s and a launch angle of 62 degrees, we can find the time the ball is in the air as follows:
- First, calculate the initial vertical velocity component (v_y) using the sine function: v_y = v * sin(θ).
- Then, use the time of flight equation with v_y to calculate the total time in air.
Doing the math:
- v_y = 18 m/s * sin(62°) = 18 * 0.882 = 15.876 m/s
- t = (2 * 15.876 m/s) / 9.8 m/s² = 31.752 / 9.8 ≈ 3.24 s
The ball will be in the air for approximately 3.24 seconds.