A golf ball is hit off a tee at the edge of a cliff. Its x and y coordinates as functions of time are given by x = 19.4t and y = 3.72t − 4.93t2,where x and y are in meters and t is in seconds.
x = 19.4t and y = 3.72t − 4.93t^2
You have stated some facts about the ball's trajectory. Now what is the question?
To find how far the golf ball traveled horizontally before hitting the ground, we need to find the time when it hits the ground.
To do this, we set the y-coordinate equal to zero (since hitting the ground means y = 0) and solve for t:
0 = 3.72t - 4.93t²
This equation is a quadratic equation. We can either use factoring or the quadratic formula to solve for t.
Let's use the quadratic formula:
t = (-b ± √(b² - 4ac)) / (2a)
Here, a = -4.93, b = 3.72, and c = 0. Plugging these values into the formula, we get:
t = (-3.72 ± √(3.72² - 4(-4.93)(0))) / (2(-4.93))
Simplifying further,
t = (-3.72 ± √(13.81)) / (-9.86)
Now, we can calculate the values of t:
t₁ = (-3.72 + √(13.81)) / (-9.86)
t₂ = (-3.72 - √(13.81)) / (-9.86)
Since the question asks for the positive value of t, we will discard the negative value. So, t = t₁.
Next, we substitute this value of t back into the x-coordinate equation to find the distance traveled horizontally:
x = 19.4t
Substituting t = t₁, we get:
x = 19.4(t₁)
Calculate the value of t₁ using a calculator and multiply it by 19.4 to get the horizontal distance traveled by the golf ball.