Jim has a difficult golf shot to make. His ball is 100m from the hole. He wants the ball to land 5m in front of the hole, so it can role to the hole. A 20m tree is between his ball and the hole, 40m from the hole and 60m from Jim's ball. With the base of the tree as the origin, write an algebraic expresion to model the height of the ball if it just clears the top of the tree.
cry
To write an algebraic expression to model the height of the ball if it just clears the top of the tree, let's break down the problem.
We know that Jim wants the ball to land 5m in front of the hole. Since the ball is currently 100m from the hole, the total distance the ball needs to travel is 100m + 5m = 105m.
Now, we have a right triangle where the base is the tree, a side is the distance between the tree and the hole (40m), and the hypotenuse is the distance between Jim's ball and the hole (60m). We can use the Pythagorean theorem to find the height of the tree.
Using the Pythagorean theorem, we have:
(tree)^2 + (40m)^2 = (60m)^2
Simplifying this equation, we get:
(tree)^2 + 1600m^2 = 3600m^2
Subtracting 1600m^2 from both sides, we have:
(tree)^2 = 2000m^2
Taking the square root of both sides to solve for the height of the tree, we get:
tree = √2000m
Therefore, the algebraic expression to model the height of the ball if it just clears the top of the tree is:
height = √2000m.