Final answer:
To find the time the object will be in the air, we can use the equations of motion for projectile motion. Given the initial speed and launch angle, we can calculate the initial vertical velocity. Using the initial height and the equation for vertical displacement, we can determine the time the object will be in the air.
Step-by-step explanation:
To find the time the object will be in the air, we can use the equations of motion for projectile motion. First, we need to determine the vertical component of the object's initial velocity. We can use the equation v = v0sin(θ) to find the vertical component, where v is the initial velocity, v0 is the initial vertical velocity, and θ is the launch angle. Plugging in the values, we get v0 = 4.44 m/s * sin(23.0°) = 1.84 m/s.
Now, we can use the equation h = v0t - 1/2gt^2, where h is the initial height, v0 is the initial vertical velocity, t is the time, and g is the acceleration due to gravity. Plugging in the values, we get 183 m = 1.84 m/s * t - 1/2 * 9.8 m/s^2 * t^2. Rearranging the equation and solving for t, we get a quadratic equation: -4.9t^2 + 1.84t - 183 = 0.
Solving this equation using the quadratic formula, we find two solutions for t: t = 11.38 s and t = -3.18 s. Since time cannot be negative, we discard the negative solution. Therefore, the object will be in the air for approximately 11.38 seconds.