Parametric

[sarahsham]

Luisa begins her 10 meter platform dive with a velocity of about 2.3 meters per sec. The angle at which Luisa leaves the platform is about 85 degrees with the horizontal.
About how long is she in the air?

For this question, I came up with a parametric equation to find her position.
It is:
x(t)=(2.3T)Tcos(85)
y(t)=(2.3T)Tsin(85)-4.9T^2 +10

SO, to find how long she's in the air, I made those equation equal to 0 and I don't know. The answer is 0? I don't even know what to do for this problem.

 

[mmm4444bot]

?

I came up with [parametric equations] to find her position.

x(t) = 2.3 cos(85°) t

y(t) = 2.3 sin(85°) t - 4.9 t^2 + 10

In each equation, you had an extra factor of t. I removed them (above).

I made those equation equal to 0

No, don't set both of them equal to zero. Only the vertical component goes to zero.

\(\displaystyle h(t) \ = \ -4.9 \ t^2 \ + \ v_0 \cdot t \ + \ h_0\)

\(\displaystyle \text{Initial vertical velocity:} \ v_0 = 2.3 \ sin(85^{\circ}) \ \text{meters per second}\)

\(\displaystyle \text{Initial height:} \ h_0 = 10 \ \text{meters}\)

\(\displaystyle y(t) \ = \ -4.9 \ t^2 \ + \ [ 2.3 \ sin(85^{\circ}) ] \ t \ + \ 10\)

Hi Sarah:

Solving the equation y(t) = 0 gives the number of seconds required for the diver's height to become zero (i.e., the elapsed time before hitting the surface of the water).

In other words, this value of t is the number of seconds that the diver remains in the air.

You don't need to use x(t) .

MY EDITS: Previously missed an extra factor of t; fixed ambiguous wording

 

[sarahsham]

Re:

I came up with [parametric equations] to find her position.

x(t) = 2.3 t cos(85°)

y(t) = 2.3 t sin(85°) - 4.9 t^2 + 10

In each equation, you had an extra factor of t. I removed them.

I made those equation equal to 0

No, don't set both of them equal to zero. Only the vertical goes to zero.

Hi Sarah:

Solving the equation y(t) = 0 gives us the number of seconds required for the diver's height to be zero meters above the surface of the water (i.e., "ground level").

In other words, that solution for t is the number of seconds that the diver remains in the air, before hitting the water.

Is this exercise asking for the horizontal location as well (i.e., both coordinates at the entry point) ?

If not, you won't be using x(t).

Cheers ~ Mark

Hm, I see what you're saying but this question has more parts to it.
1) How long is she in the air
- For this, I don't solve for 0?

2) How high above the platform is she before she starts moving toward the water?
- Do I solve for 10?

3) How far does she move horizontally before hitting the water?
- So I guess I would have to use x(t) right? I don't even know what to do to find the answer

4) How many meters is luisa from the platform when she passes it during the dive?
- I think this one is like part 3 but like part 3, I don't have any idea how to even write my equations to solve for the answer

5) If the pushoff angle were changed to 80 degrees, how close to the platform would she come?
- yeah. I don't know how to do this too.

I know it seems like I want to know answers but the truth is, I really really want to know how to do it and an explanation. I can't seem to find the right person to explain it to me in a way that I understand. Please help?

 

[mmm4444bot]

1) How long is she in the air

- For this, I don't solve for 0? No, you DO solve for zero.

Specifically, you solve the equation y(t) = 0 for t.

What I told you not to do is: do not use x(t) for trying to find how long she's in the air.

2) How high above the platform is she before she starts moving toward the water?

This is the same as asking what her distance is from the platform to the highest point during the dive, yes?

Can you find the vertex of a parabola?

3) How far does she move horizontally before hitting the water?

- So I guess I would have to use x(t) right? Exactly. But you first need the number of seconds rom part (1), before you can evaluate x(t) to get the horizontal position at the entry point.

4) How many meters is luisa from the platform when she passes it during the dive?

For this, you want to solve for the height y(t) again, yes.

What is the value of y(t) when she passes the platform. That's the value to which you need to set y(t), and solve for t.

5) If the pushoff angle were changed to 80 degrees, how close to the platform would she come?

I don't know how to do this too.

You need to start over with a new definition for the height function y(t) because the vertical component of the initial velocity has a new value every time the angle changes.

Let's get the first part finished first. Okay?

If you would like to interact live, I'm at pathwhelp.org (Teacher/Tutor/Student chat room).

Click on the [Live Help!] button.

Otherwise, how about you start by evaluating 2.3 sin(85°), and then using the decimal approximation in the Quadratic Formula, when you solve y(t) = 0 .

Show me what you get.

If I wrote anything that you do not understand, then please ask specific questions (either by posting them here, or entering the chat room at the URL above during the next several minutes).

Cheers ~ Mark