Question

Please help? Parametric equations

Suppose that Tiger hit a golf ball with an initial velocity of 150 ft/sec at an angle of elevation of
30°. Write the parametric equations to represent the flight of the ball. How long is the golf ball in the air? Determine the distance the ball traveled. When is the ball at its maximum height? What is the maximum height?

Answer 1

@cdosborn is it
x(t) = 150 cos 30° t
y(t) = 150 sin 30° t - 16 t^2

Answer 2

What is your rational behind the 16, in y(t). Recall:
\[y(t) = y_0 + v_{0y}t + \frac{ 1 }{ 2 } a_yt^2\]

Answer 3

rationale*

Answer 4

Your x(t) is spot on

Answer 5

how do i find the last 4 questions? the " How long is the golf ball in the air? Determine the distance the ball traveled. When is the ball at its maximum height? What is the maximum height?" @cdosborn

Answer 6

Your y(t) is not right, so you will not be able to solve the problems.

How long is the ball in the air?
y(t) relates the height of the ball with the time. Ideally you'd like to know the time that the height was 0. Which is simple just set y(t) = 0, and solve for a value of t, that makes it true. Know that at t=0, the height should also be 0. There are two solutions which both make sense.

How far did it travel?
Well if we know how long it was in the air, ex. 5 sec. And we have an eqn which tells us its x position (or distance) for any given time. We just use our x(t) function for the final distance at the final time.

What is the time of max height?
Well, you know that the shape of the flight has to be a parabola. This means that half the time it was going higher to its max height and then spent the other half of the time coming back to the ground

What is the max height?
You should know at what time it was at its max height (the question before) if you plug that time into your eqns you can find out its distance from the tiger (x position) or its height (y position)