Question

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​​

Answer 1

here ya go!

Explanation:

Answer 2

The line travels a horizontal distance of approximately 18 meters and reaches its maximum height after approximately 1.3 seconds.

To find the horizontal distance traveled by the line, we need to find the value of x when y = 0.

So, we set y(t) = 0 and solve for t: -9.812 + (30sin(60°))t + 1 = 0. Solving this equation gives t ≈ 2.6 seconds.

Now, substitute this value of t into the x(t) equation to find x(2.6): x(2.6) = (30cos(60°))(2.6) ≈ 18 meters.

To find the time it takes for the line to reach its maximum height, we need to find the value of t when the vertical velocity vy = 0.

So, solve the equation: -9.812 + (30sin(60°))t + 1 = 0. Solving this equation gives t ≈ 1.3 seconds.