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Applications of parametric curves are considered in detail
Chapter 13, Problem 56E(choose chapter or problem)
Applications of parametric curves are considered in detail in Section 11.7.
Golf slice A golfer launches a tee shot down a horizontal fairway and it follows a path given by \(\mathbf{r}(t)=\left\langle a t,(75-0.1 a) t,-5 t^{2}+80 t\right\rangle\), where \(t \geq 0\) measures time in seconds and r has units of feet. The y-axis points straight down the fairway and the z-axis points vertically upward. The parameter a is the slice factor that determines how much the shot deviates from a straight path down the fairway.
a. With no slice (a = 0), sketch and describe the shot. How far does the ball travel horizontally (the distance between the point the ball leaves the ground and the point where it first strikes the ground?
b. With a slice (a = 0.2), sketch and describe the shot. How far does the ball travel horizontally?
c. How far does the ball travel horizontally with a = 2.5?
Questions & Answers
QUESTION:
Applications of parametric curves are considered in detail in Section 11.7.
Golf slice A golfer launches a tee shot down a horizontal fairway and it follows a path given by \(\mathbf{r}(t)=\left\langle a t,(75-0.1 a) t,-5 t^{2}+80 t\right\rangle\), where \(t \geq 0\) measures time in seconds and r has units of feet. The y-axis points straight down the fairway and the z-axis points vertically upward. The parameter a is the slice factor that determines how much the shot deviates from a straight path down the fairway.
a. With no slice (a = 0), sketch and describe the shot. How far does the ball travel horizontally (the distance between the point the ball leaves the ground and the point where it first strikes the ground?
b. With a slice (a = 0.2), sketch and describe the shot. How far does the ball travel horizontally?
c. How far does the ball travel horizontally with a = 2.5?
ANSWER:Solution 56EStep 1:Applications of parametric curves are considered in detail in Section.Golf slice A golfer launches a tee shot down a horizontal fairway; it follows a path given by r(t) = at,(75 – 0.1a)t, - 5t2 + 80t where t 0 measures time in seconds and r has units of feet.The y-axis points straight down the fairway and the z-axis points vertically upward. The parameter a is the slice factor that determines how much the shot deviates from a straight path down the fairway.Step 1:(a). With no slice (a = 0), sketch and describe the shot. How far does the ball travel horizontally (the distance between the point the ball leaves the ground and the point where it first strikes the ground)At we get the path The graph of the curve is To find the distance between the point the ball leaves the ground and the point where it first strikes the ground.At the point where the ball touches the ground the z-axis will be 0.Therefore Since the ball travels in the y-axis the distance travelled by the ball will be