Final answer:
To find the minimum speed of the round before it strikes the ground, we need to consider both the vertical motion caused by gravity and the horizontal motion caused by the wind. We can calculate the time it takes for the round to reach the ground using kinematic equations and determine the horizontal distance traveled by using the wind speed. Finally, we can combine the vertical and horizontal components to find the minimum speed using the Pythagorean theorem.
Step-by-step explanation:
To find the minimum speed of the round before it strikes the ground, we need to consider both the vertical motion caused by gravity and the horizontal motion caused by the wind. Since the round is fired straight up, its initial vertical velocity is zero. As it travels upward, it will accelerate downward due to the force of gravity. At the peak of its trajectory, its vertical velocity will be at its maximum. When the round starts to fall back down, its vertical velocity will increase until it strikes the ground.
On the other hand, the wind blowing in the northwest direction will cause the round to move horizontally as it falls. The horizontal distance it travels before striking the ground depends on the time it takes to reach the ground and the horizontal speed given by the wind.
To calculate the minimum speed of the round, we need to consider the components of its motion separately and then combine them. First, we can determine the time it takes for the round to reach the ground by using kinematic equations for vertical motion. Next, we can find the horizontal distance traveled by using the horizontal speed given by the wind and the time calculated previously. Finally, we can combine the vertical and horizontal components to find the minimum speed using the Pythagorean theorem.