How do I solve parts D and E for 54? Certainly! Here's a transcription suitable for an educational website:---**Section 10.6: Plane Curves and Parametric Equations****Problem 54:**Tony hits a baseball at a height of 3 ft from the ground. The ball leaves his bat traveling with an initial speed of 120 ft/sec at an angle of 45° from the horizontal. Choose a coordinate system with the origin at ground level directly under the point where the ball is struck.- **a.** Write parametric equations that model the path of the ball as a function of time $ t $ (in sec).- **b.** When is the ball at its maximum height? Give the exact value and round to the nearest hundredth of a second.- **c.** What is the maximum height?- **d.** If an outfielder catches the ball at a height of 6 ft, for how long was the ball in the air after being struck? Give the exact answer and the answer rounded to the nearest hundredth of a second.- **e.** How far is the outfielder from home plate when he catches the ball? Round to the nearest foot.**Problem 56:**Two planes flying at the same altitude are on a course to fly over a control tower. Plane A is 50 mi east of the tower flying 125 mph. Plane B is 90 mi south of the tower flying 200 mph. Place the origin of a rectangular coordinate system at the intersection.- **a.** Write parametric equations that model the path of each plane as a function of the time $ t \ge 0 $ (in hr).- **b.** Determine the times required for each plane to reach a point directly above the tower. Based on these results, will the planes crash?- **c.** Write the distance between the planes as a function of the time $ t $.- **d.** How close do the planes pass? Round to the nearest tenth of a mile.**Problem 58:**A daredevil wants to jump over a canyon on his motorcycle. He travels approximately 88 ft/sec (60 mph) at an angle of 30° when the motorcycle leaves the ramp.---This transcription provides the necessary information for students or educators to work on the problems related to parametric equations and motion analysis.

For finding parametric equation,The vertical position is given by, x=v0cosθt And horizontal position is given by, y = -16t2+v0sinθt +hwhere t is time, θ is angle and v0 is initial speed.Substituting the values for finding time t,x=120cos45°ty= -16t2+120sin45°t +6Set yt=0, for finging time t.⇒16t2-84.85t -6=0Solving this quadratic equation, we get.t=5.35379 sec.~6 sec.Outfielder takes 6 sec to catch the ball. y=Maximum height ymax=v0sinα22g where v0 is initial speed and α is the angle. Here, v0=120 ft/sec and α=45° ymax=120sin45°229.81=84.85219.62=7,199.919.62=366.95~400 ft x=Rangewidth of ground is, R=v02gsin2θ=12029.81sin2(45°)=14,4009.81sin90°=1,467.89~1500 ft Now, substitute x=1500 in x= 120cos45°tt=150084.85=17.68 sec~18 sec Substitute t in y= -16t2+120sin45°t +6=-1617.682+84.85×17.68+6=-5,001.32+1,506.15=3,495.17~3500 ft.Outfielder is at 3500 ft from home plate, when he catches the ball.

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d. If an outfielder catches the ball at a height of 6 ft, for how long was the ball in the air after being struck? Give the exact answer and the answer rounded to the nearest hundredth of a second. e. How far is the outfielder from home plate when he catches the ball? Round to the nearest foot.

d. If an outfielder catches the ball at a height of 6 ft, for how long was the ball in the air after being struck? Give the exact answer and the answer rounded to the nearest hundredth of a second. e. How far is the outfielder from home plate when he catches the ball? Round to the nearest foot.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

How do I solve parts D and E for 54?

Certainly! Here's a transcription suitable for an educational website:

---

**Section 10.6: Plane Curves and Parametric Equations**

**Problem 54:**

Tony hits a baseball at a height of 3 ft from the ground. The ball leaves his bat traveling with an initial speed of 120 ft/sec at an angle of 45° from the horizontal. Choose a coordinate system with the origin at ground level directly under the point where the ball is struck.

- **a.** Write parametric equations that model the path of the ball as a function of time $ t $ (in sec).
- **b.** When is the ball at its maximum height? Give the exact value and round to the nearest hundredth of a second.
- **c.** What is the maximum height?
- **d.** If an outfielder catches the ball at a height of 6 ft, for how long was the ball in the air after being struck? Give the exact answer and the answer rounded to the nearest hundredth of a second.
- **e.** How far is the outfielder from home plate when he catches the ball? Round to the nearest foot.

**Problem 56:**

Two planes flying at the same altitude are on a course to fly over a control tower. Plane A is 50 mi east of the tower flying 125 mph. Plane B is 90 mi south of the tower flying 200 mph. Place the origin of a rectangular coordinate system at the intersection.

- **a.** Write parametric equations that model the path of each plane as a function of the time $ t \ge 0 $ (in hr).
- **b.** Determine the times required for each plane to reach a point directly above the tower. Based on these results, will the planes crash?
- **c.** Write the distance between the planes as a function of the time $ t $.
- **d.** How close do the planes pass? Round to the nearest tenth of a mile.

**Problem 58:**

A daredevil wants to jump over a canyon on his motorcycle. He travels approximately 88 ft/sec (60 mph) at an angle of 30° when the motorcycle leaves the ramp.

---

This transcription provides the necessary information for students or educators to work on the problems related to parametric equations and motion analysis.

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