Projectile motion of mortar round problem

[jjones1573]

Homework Statement

A mortar round is fired over a building that is 2600m away, at an initial velocity of 240m/s. The building is 1600m tall and 100m wide. Calculate the distances which are safe from mortar shells left of the building.

Homework Equations

1.) Vy(t) = Vyo - at

2.) Sy(t) = Syo + Vyo - 0.5at^2

The Attempt at a Solution

I can use the above equations to find an angle by guessing a distance where the projectile lands to then calculate the max height of the arc and see if it could clear the building but it seems like this would be doing it the wrong way around as I would have to keep making guesses.

Is there some way I could factor in the height of the building to my equations?

 

[lewando]

The phrase "left of the bulding" is seriously not helpful. If (x,y) = (0,0) is the origin, located at the mortar, where "up" is +y and "to the right" is +x, then, assuming the building is centered at 2600m to the right of the mortar, any trajectory that falls short of the point (2550,0) and exceeds the point (2650,1600) will be safe, from the building's point of view.

 

[jjones1573]

Sorry that was meant to be right of the building, where the building is to the right of the mortar origin.

 

[jjones1573]

I can't edit the post but the mortar is at the origin and the building is 2600m on the positive x-axis from the origin.

I'm still pretty stumped with this. I could make guesses at the angle or the distance it lands but I don't know how I could be more precise?

 

[rwisz]

As a scientist, we can approach this problem by first analyzing the initial conditions of the mortar round. The given initial velocity of 240m/s and the distance of 2600m suggest that the mortar round is fired at an angle of approximately 5.5 degrees above the horizontal.

Next, we can use the equations of projectile motion to calculate the maximum height of the mortar round's trajectory. This can be done by finding the time it takes for the round to reach its peak height, which can be found by setting the vertical velocity (Vy) to zero in equation 1. Once we have the time, we can plug it into equation 2 to find the maximum height (Sy).

Now, to determine the safe distances from the building, we need to consider the height and width of the building. The maximum height of the mortar round's trajectory needs to be at least 1600m above ground level to clear the building. Using this information, we can set up a trigonometric equation to find the distance from the building where the maximum height is 1600m. This will give us the minimum safe distance from the building.

Additionally, we can also consider the width of the building to determine the safe distances. Depending on the angle of the mortar round, it may also be necessary to consider the width of the building when calculating the safe distances.

In summary, by using the equations of projectile motion and considering the height and width of the building, we can accurately calculate the safe distances from the building for the given mortar round problem. It is important to carefully analyze the initial conditions and consider all factors in order to arrive at an accurate solution.