To find where the ball will land, we need to find the x-coordinate when y = 0 on the path of the ball.
Setting y = 0 in the equation y =− 0.005x^2 + 0.7x + 3.5, we get:
0 =− 0.005x^2 + 0.7x + 3.5
Multiplying by 200 to clear decimals:
0 =− x^2 + 140x + 700
Rearranging to standard form:
x^2 - 140x - 700 = 0
Now, we can solve this quadratic equation using the quadratic formula:
x = (140 ± √(140^2 - 4(1)(-700))) / (2(1))
x = (140 ± √(19600 + 2800)) / 2
x = (140 ± √22400) / 2
x = (140 ± 149.67) / 2
We have two possible solutions:
x = (140 + 149.67) / 2 = 289.67 / 2 = 144.8
x = (140 - 149.67) / 2 = -9.67 / 2 = -4.8
Given that distance cannot be negative, the ball will land approximately 4.8 feet from the batter. Therefore, the answer is b. 4.8 feet.
A batter strikes a baseball. The equation y =− 0. 005x models its 2 + 0. 7x + 3. 5 path, where x is the horizontal distance, in feet, the ball travels and y is the height, in feet, of the ball. How far from the batter will the ball land? Round to the nearest tenth of a foot. a. -4.8 feet b. 4.8 feet c. 145.9 feet d. 144.8 feet
1 answer