Final answer:
To determine the time the shell is in the air and how far it goes, we can use the equations of projectile motion. By analyzing the vertical and horizontal motion separately, we can calculate the initial vertical velocity, time of flight, initial horizontal velocity, and horizontal distance travelled. The initial vertical velocity is determined using the initial velocity and launch angle, while the time of flight is calculated using the initial vertical velocity and the acceleration due to gravity. The initial horizontal velocity is found using the initial velocity and launch angle, and the horizontal distance is determined using the initial horizontal velocity and time of flight.
Step-by-step explanation:
To determine how long the shell is in the air and how far it goes, we can use the equations of projectile motion. We will consider the vertical and horizontal motion separately.
First, let's analyze the vertical motion. We know that the initial vertical velocity is given by the equation:
Vi = V * sin(θ)
where Vi is the initial vertical velocity, V is the initial velocity of the shell, and θ is the launch angle. Plugging in the given values, we have:
Vi = 1500 m/s * sin(55°)
Next, we can use the equation for the time of flight:
T = 2 * Vi / g
where T is the time of flight and g is the acceleration due to gravity (9.8 m/s^2). Plugging in the calculated value of Vi, we can solve for T.
Now let's analyze the horizontal motion. The initial horizontal velocity is given by the equation:
Vh = V * cos(θ)
where Vh is the initial horizontal velocity. Plugging in the given values, we have:
Vh = 1500 m/s * cos(55°)
To find the horizontal distance travelled, we can use the equation:
D = Vh * T
where D is the horizontal distance. Plugging in the calculated values of Vh and T, we can solve for D.