Graphing Parametric Equations: Describing Projectile Motion

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

1. y(t) = 0, -9.81t² + 30sin60°t + 1 = 0, t = 2.686 s; s = x(2.686) = -9.81· 2.686² + 30sin60°·2.686 = 40 m

Answer is D.

2. Velocity v_y = 30sin60° - 9.81t = 0; t = 30sin60°/9.81 = 2.6 s; Answer is B.