The height y (in feet) of a baseball thrown by a child is
y = -1/10 x^2 + 3x + 6
where x is the horizontal distance (in feet) from where the ball was thrown.
Will the ball fly over the head of another child 30 feet away trying to catch the ball?
(Assume that the child who is trying to catch the ball holds a baseball glove at a height of 5 feet.)
y = ( - 1 / 10 ) x ^ 2 + 3 x + 6
for x = 30 ft
y = ( - 1 / 10 ) * 30 ^ 2 + 3 * 30 + 6 =
( - 1 / 10 ) * 900 + 90 + 6 =
- 900 / 10 + 90 + 6 =
- 90 + 90 + 6 = 6 ft
6 ft > 5 ft
The ball will fly over the head of another child.
Well, let's find out! If we substitute the value of x as 30 feet into the equation, we can determine the height of the ball at that distance.
y = -1/10 x^2 + 3x + 6
y = -1/10 (30)^2 + 3(30) + 6
y = -1/10 (900) + 90 + 6
y = -90 + 90 + 6
y = 6
So, the height of the ball when it reaches a distance of 30 feet is 6 feet. Since the child trying to catch the ball holds the glove at a height of 5 feet, the ball will indeed fly over their head. Looks like they might need a step ladder to catch that one!
To determine if the ball will fly over the head of another child who is 30 feet away, we need to find the height of the ball when it reaches 30 feet horizontally.
Substitute x = 30 into the equation y = -1/10 x^2 + 3x + 6:
y = -1/10 (30)^2 + 3(30) + 6
= -1/10 (900) + 90 + 6
= -90 + 90 + 6
= 6
The height of the ball when it reaches 30 feet horizontally is 6 feet.
Since the child who is trying to catch the ball holds a baseball glove at a height of 5 feet, and the ball will be at a height of 6 feet, the ball will indeed fly over the head of the child trying to catch it.
To determine whether the ball will fly over the head of the child 30 feet away trying to catch the ball, we need to find the height of the ball at that distance and compare it to the height of the child's glove.
First, let's substitute x = 30 into the equation for y to find the height of the ball at that distance:
y = -1/10(30)^2 + 3(30) + 6
y = -1/10(900) + 90 + 6
y = -90 + 90 + 6
y = 6
So, the height of the ball at a horizontal distance of 30 feet is 6 feet.
Now, we compare this height to the height of the child's glove, which is 5 feet. Since the height of the ball is greater than the height of the glove, we can conclude that the ball will indeed fly over the head of the child trying to catch it.