To find the horizontal distance the rock will travel, we need to find the value of x when y is equal to zero (since the rock will be at ground level when it lands). So we set y equal to zero and solve for x:
0 = -0.005x² + 0.42x - 6.5
We can use the quadratic formula to solve for x:
x = [-0.42 ± sqrt((0.42)² - 4(-0.005)(-6.5))]/(2(-0.005))
x = [-0.42 ± sqrt(0.7396)]/(-0.01)
x = [-0.42 ± 0.86]/(-0.01)
We can discard the negative solution (since distance cannot be negative) and simplify:
x = (-0.42 + 0.86)/(-0.01)
x = 44
Therefore, the rock will land 44 feet horizontally from Landon. The closest answer choice is 20.46 ft (b), but this is incorrect. The correct answer is (none of the above) 44 ft.
Landon is standing in a hole that is 6.5 ft deep. He throws a rock, and it goes up into the air, out of the hole,
and then lands on the ground above. The path of the rock can be modeled by the equation y = -0.005x² +
0.42x- 6.5, where x is the horizontal distance of the rock, in feet, from Landon and y is the height, in feet, of
the rock above the ground. How far horizontally from Landon will the rock land?
a. 63.54 ft c. 10.23 ft
b. 20.46 ft d. 31.77 ft
1 answer
1 answer