Answer: (10.4, 0).
Step-by-step explanation: In order to determine the coordinate where the projectile would land, we need to find the parabolic path followed by the projectile. Since the catapult is launched from the origin (0,0), and has a maximum height at (5.2, 6.3), we can find the vertex of the parabola, which is also (5.2, 6.3).
The standard form of a parabola is y = a(x - h)^2 + k, where (h,k) is the vertex of the parabola. In this case, h = 5.2 and k = 6.3.
We can use the information from the origin to determine the value of 'a'. Substituting x = 0 and y = 0, we get:
0 = a(0 - 5.2)^2 + 6.3
Solving for 'a':
a(5.2)^2 = -6.3
a = -6.3 / (5.2)^2
Now that we have 'a', we can rewrite the equation of the parabola:
y = a(x - 5.2)^2 + 6.3
To find the x-coordinate where the projectile would land, we need to find the other x-intercept (the other point where y = 0). Since the parabola is symmetric, the other x-intercept will be equidistant from the vertex:
x = 5.2 * 2 = 10.4
Now, we can plug in x = 10.4 into the equation to find the y-coordinate:
y = a(10.4 - 5.2)^2 + 6.3
However, since we are looking for the landing coordinate, which is an x-intercept, we know the y-coordinate will be 0.
Thus, the coordinate where the projectile would land is (10.4, 0).