A battleship simultaneously fires two shells toward two identical enemy ships. One shell hits ship A, which is close by, and the other hits ship B, which is farther away. The two shells are fired at the same speed. Assume that air resistance is negligible and that the magnitude of the acceleration due to gravity is g .
1.Which shell is launched with a greater horizontal velocity, v2?
2. Which shell reaches the greater maximum height?
3.
Which shell has the longest travel time (time elapsed between being fired and hitting the enemy ship)?
3.
To answer these questions, we need to analyze the projectile motion of the shells. In projectile motion, an object is launched into the air at an angle and follows a curved path due to the force of gravity.
1. To determine which shell is launched with a greater horizontal velocity, v2, we need to consider the horizontal component of the velocity. Since both shells are fired with the same speed, the only factor affecting the horizontal velocity is the launch angle. The shell that hits ship A, which is closer, will have a smaller launch angle compared to the shell that hits ship B, which is farther away. Therefore, the shell that hits ship B will have a larger horizontal velocity, v2.
2. To determine which shell reaches a greater maximum height, we need to analyze the vertical component of the motion. Both shells have the same initial vertical velocity (zero), and the time taken to reach the maximum height is determined by the vertical motion. The time of flight for each shell will depend on their respective launch angles and the acceleration due to gravity. However, since both shells are fired at the same speed, the shell with a larger launch angle (the one hitting ship B) will have a greater time of flight and will ultimately reach a greater maximum height compared to the shell hitting ship A.
3. To determine which shell has the longest travel time, we need to consider the total time of flight for each shell. The total time of flight is the sum of the time taken to reach the maximum height and the time taken to reach the target. Since the shell hitting ship B has a larger time of flight to reach the maximum height, it will also have a longer total travel time compared to the shell hitting ship A.
In summary:
1. The shell hitting ship B is launched with a greater horizontal velocity, v2.
2. The shell hitting ship B reaches a greater maximum height.
3. The shell hitting ship B has the longest travel time.