Question

The trajectory of a potato launched from a potato cannon on the ground at an angle of 45 degrees with a speed of 65 meters per second can be modeled by the parabola: y=x-0.0023x^2, where the x-axis is the ground. Find the height point of the trajectory and the horizontal distance the potato travels before hitting the ground.

Answer 1

Explanation:

The highest point of a parabola is at the vertex.

x = -b / (2a)

x = -1 / (2×-0.0023)

x ≈ 217.4

y = (217.4) − 0.0023 (217.4)²

y ≈ 108.7

The horizontal distance can be found when the potato lands (y=0):

0 = x − 0.0023x²

0 = x (1 − 0.0023x)

x = 0, x ≈ 434.8

So the potato reaches a maximum height of 108.7 m and travels a horizontal distance of 434.8 m.