Final answer:
To find the time a shell is in motion after being fired at an angle, you calculate the vertical component of its initial velocity and apply the motion equations for a projectile. The flight time is twice the time it takes to reach the peak, which is calculated using the initial vertical velocity divided by the acceleration due to gravity.
Step-by-step explanation:
To calculate the time the shell is in motion, we need to consider the vertical component of the shell's initial velocity. The initial velocity can be broken down into horizontal and vertical components using trigonometry. Since the shell is launched at an angle to the horizontal, we use the sine function to calculate the vertical component (V_vertical = V_initial × sin(θ)).
For a projectile launched and landing at the same height and ignoring air resistance, the time it spends in the air is given by the formula T = 2 × V_vertical / g, where g is the acceleration due to gravity (approximately 9.81 m/s²). We use this formula because the shell takes equal time to rise to its highest point and to fall back down.
Using these concepts, we can solve for the time in motion:
- V_vertical = 1.7 × 10³ m/s × sin(55°)
- T = 2 × V_vertical / g
By performing the calculations with the given values, we obtain the duration that the shell is in motion. Note that similar steps would apply to the examples provided in your question, differing mainly in the velocity and angle values.