Physics 1 Parabolic Motion Question Confusion

[Confused_Student33]

Problem: A small forest animal jumps with an initial speed of v0 = 15.0m/s and travels to a maximum height of 2.160m. What horizontal distance would the animal travel if the launch angle is i) 45.0 degrees or ii) 42.0 degrees?

Correct Answer: i) 24.95m ii) 25.02m

My professor solved this by: Change in y = 0 - 2.16m

-2.16m = (15Sin45)t + .5gt^2 ----- Use Quadratic to solve for t
R = (15Cos45)t ----- Plug in t to solve for range

I'm confused on why he used Viy = 2.160m

My understanding is that this animal initially jumped from an unknown height to 2.16m. Shouldn't Viy be the unknown height instead of 2.16m? Since he is using 2.16m as a starting point, is the distance the animal traveled before it reaches 2.16m ignored? Wouldn't using 2.16m as a starting point also ignore the time it took before he reached his max height?

 

[BvU]

Hi, and

​

initially jumped from an unknown height to 2.16m

How high does one jump if starting (straight up) from zero with a speed of 15 m/s ?

$\$

 

[haruspex]

from an unknown height

You can assume the given height is measured from the jumping point. What is unknown is the angle.

 

[BvU]

I'm confused on why he used Viy = 2.160m

I don't see that in your scenario ??

-2.16m = (15Sin45)t + .5gt^2 ----- Use Quadratic to solve for t
R = (15Cos45)t ----- Plug in t to solve for range

Strange. If the initial speed is $v_0 = 15$ m/s, and the initial angle is 45 degrees, I would expect a total time in the air to follow from $v_0 \sin({\pi\over 4})\, t -{1\over 2} g t^2 = 0$ and the horizontal distance travelled from
$x = v_0\cos ({\pi\over 4})\, t$

 

[BvU]

Ah, there seems to be something going wrong here. The

Correct Answer: i) 24.95m ii) 25.02m

suggests a much greater height is reached than the 2.16 m in the story.

And that 42 degrees should give a longer jump than 45 degrees is something I don't understand either.

$\$

 

[haruspex]

To get the given answers, interpret it thus:

Edit: correction…

The 2.16m is not the max height of the jump, it is the landing height below the starting point in both cases. I.e. the height gain is -2.16m.
The range is maximised when $2\sin^2(\theta)=\frac 1{1-hg/v^2}$, about 42.5° here.

g is 9.8m/s^2, not 9.81.

 

[nasu]

And you get 24.95 for the $45^o$ angle?
Assuming that it land on the way down, I get 28.1 m.
It could also land there on the way up and then the horizontal range is just 3.3 m.

 

[haruspex]

And you get 24.95 for the $45^o$ angle?
Assuming that it land on the way down, I get 28.1 m.
It could also land there on the way up and then the horizontal range is just 3.3 m.

See my correction.

 

[nasu]

What correction?

 

[haruspex]

What correction?

The 2.16m is not the max height of the jump, it is the landing height below the starting point in both cases. I.e. the height gain is -2.16m.

Originally it read as though the 2.16m was above the launch point.

 

[PeroK]

Problem: A small forest animal jumps with an initial speed of v0 = 15.0m/s and travels to a maximum height of 2.160m. What horizontal distance would the animal travel if the launch angle is i) 45.0 degrees or ii) 42.0 degrees?

Correct Answer: i) 24.95m ii) 25.02m

No animal can jump anything like that distance! Especially small forest animals.

 

[haruspex]

No animal can jump anything like that distance!

Well, it could if it takes off at 15m/s (running start?) and the landing point is 2m below launch (which is what the question has to mean to get this answer, though I suspect that is just a sign error in the solution).

 

[PeroK]

Well, it could if it takes off at 15m/s (running start?) and the landing point is 2m below launch (which is what the question has to mean to get this answer, though I suspect that is just a sign error in the solution).

It's jumping out of tree, perhaps? It would need to avoid all the other trees within a 25m radius.

It could be a flying fox, but then the motion is not parabolic.

 

[kuruman]

So the consensus here is that the formulation of the problem should have been
"A small forest animal jumps with an initial speed of v0 = 15.0m/s and travels to a maximum drops by height of 2.160m. What horizontal distance would the animal travel if the launch angle is i) 45.0 degrees or ii) 42.0 degrees?"

That is the formulation that the professor solved, not the formulation that matches the statement of the problem. I think the correct course of action is for OP to ask the professor "In what sense does the animal travel to a maximum height of 2.160 m if its height drops by 2.160 m at the end of the jump?"

If we go along with the professor's professed solution, we will be complicit to confusing @Confused_Student33 even more. Given OP's experience with this problem, how do you think OP will interpret "maximum height" in the future?

That was my rant of the day.

 

[Confused_Student33]

Thank you for the input! I think he forgot to double the time in his answer lol. He allowed corrections and I got full credit back doing it his way, but I'll ask him in his office hours and let yall know what he says.

 

[kuruman]

Thank you for the input! I think he forgot to double the time in his answer lol. He allowed corrections and I got full credit back doing it his way, but I'll ask him in his office hours and let yall know what he says.

Great! I am curious to see what he says.