Graphing Parametric Equations

[Terrabow]

A fly-fishing line is cast in a parabolic motion with an initial velocity of 30 meters per second at an angle of 60° to the horizontal and an initial height of 1 meter. The following parametric equations represent the path of the end of the line: x(t) = (30cos(60°))t and y(t) = -9.812 + (30sin(60°))t + 1 Graph the parametric equations to complete the statements.

1. To the nearest meter, the line travels a horizontal distance of_____

A. 2.6
B. 18
C. 20
D. 40

2. To the nearest tenth of a second, the end of the line reaches its maximum height after_____ seconds.

A. 1.3
B. 2.6
C. 18.2
D. 40.0

 

[Harry_the_cat]

Nice question. What have you attempted?

 

[Steven G]

Shouldn't y(0) = 1?

 

[Steven G]

Two comments. Do not solve this problem by graphing as instructed. That is a terrible method, but you should also graph the function (just not to find the answer but as an exercise in graphing). 2nd comment: Please supply us with the correct equations.

 

[HallsofIvy]

Why in the world would y be given as "y= -9.812 + (30sin(60°))t + 1" and not just as "y= -8.812 + (30sin(60°))t"? Are you sure you copied that correctly?

Since this is supposed to be a parabola, perhaps it was $\displaystyle y= -8.812+ (30sin(60))(t+1)^2$?

(By the way, $\displaystyle cos(60)= \frac{1}{2}$ and $\displaystyle sin(60)= \frac{\sqrt{3}}{2}$.)

 

[Deleted member 4993]

A fly-fishing line is cast in a parabolic motion with an initial velocity of 30 meters per second at an angle of 60° to the horizontal and an initial height of 1 meter. The following parametric equations represent the path of the end of the line: x(t) = (30cos(60°))t and y(t) = -9.812 + (30sin(60°))t + 1 Graph the parametric equations to complete the statements.

1. To the nearest meter, the line travels a horizontal distance of_____

A. 2.6
B. 18
C. 20
D. 40

2. To the nearest tenth of a second, the end of the line reaches its maximum height after_____ seconds.

A. 1.3
B. 2.6
C. 18.2
D. 40.0

You say that one of the equation is:

y(t) = -9.812 + (30sin(60°))t + 1

That is not an equation for parabolic motion. If try to graph it - it will give you a straight line.

Please check your equation and post the corrected equation.

By the way - what have you done for week-old question:

Graphing Parametric Equations

A swimmer enters the water and swims in a straight line at 54 meters per minute. Another swimmer enters the water 3 minutes later, swimming in the same direction at 134 meters per minute. Which parametric equations could model the swimmers' paths from the time the first swimmer entered the...

www.freemathhelp.com

 

[Dr.Peterson]

A fly-fishing line is cast in a parabolic motion with an initial velocity of 30 meters per second at an angle of 60° to the horizontal and an initial height of 1 meter. The following parametric equations represent the path of the end of the line: x(t) = (30cos(60°))t and y(t) = -9.812 + (30sin(60°))t + 1 Graph the parametric equations to complete the statements.

1. To the nearest meter, the line travels a horizontal distance of_____

A. 2.6
B. 18
C. 20
D. 40

2. To the nearest tenth of a second, the end of the line reaches its maximum height after_____ seconds.

A. 1.3
B. 2.6
C. 18.2
D. 40.0

I suspect that

x(t) = (30cos(60°))t and y(t) = -9.812 + (30sin(60°))t + 1​

is supposed to be

x(t) = (30cos(60°))t and y(t) = -9.8t² + (30sin(60°))t + 1​

Read very carefully!

 

[Deleted member 4993]

A fly-fishing line is cast in a parabolic motion with an initial velocity of 30 meters per second at an angle of 60° to the horizontal and an initial height of 1 meter. The following parametric equations represent the path of the end of the line: x(t) = (30cos(60°))t and y(t) = -9.812 + (30sin(60°))t + 1 Graph the parametric equations to complete the statements.

1. To the nearest meter, the line travels a horizontal distance of_____

A. 2.6
B. 18
C. 20
D. 40

2. To the nearest tenth of a second, the end of the line reaches its maximum height after_____ seconds.

A. 1.3
B. 2.6
C. 18.2
D. 40.0

If the fishing pond is located somewhere on earth - that equation probably is:

y(t) = -(9.8/2)t² + (30sin(60°))t + 1

 

[Steven G]

If the fishing pond is located somewhere on earth - that equation probably is:

y(t) = -(9.8/2)t² + (30sin(60°))t + 1

By the way Mr Khan, where do you live?