Mistake in Kaplan's question of the day

[brood910]

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A toy rocket is launched at an angle of 30° above the horizontal with an initial velocity of 10 m/s. If the rocket reaches a height of 10 m, how far away does it land from the platform?

(cos 30° = 0.866, sin 30° = 0.500)

Simple question.. How can it possibly reach a height of 10m when the initial velocity is 10m/s here?

Using vf^2 = vi^2 + 2aY, (vf = 0 at the top)
we know that Y = Vi^2/2g = (10sin30)^2/2g = 25/2g = 1.25m.. So the height should have been 1.25m instead of 10m....

I didnt even have to use the height for this question, but still, why the heck did they say it reached 10m when it is not even possible?

 

[Postictal Raiden]

haha. Good catch!

 

[rjosh33]

A toy rocket is launched at an angle of 30° above the horizontal with an initial velocity of 10 m/s. If the rocket reaches a height of 10 m, how far away does it land from the platform?

(cos 30° = 0.866, sin 30° = 0.500)

Simple question.. How can it possibly reach a height of 10m when the initial velocity is 10m/s here?

Using vf^2 = vi^2 + 2aY, (vf = 0 at the top)
we know that Y = Vi^2/2g = (10sin30)^2/2g = 25/2g = 1.25m.. So the height should have been 1.25m instead of 10m....

I didnt even have to use the height for this question, but still, why the heck did they say it reached 10m when it is not even possible?

Hmmmm, it's probably a mistake on their part, but the original question mentions a platform. Did the rocket start at a height of 8.75m?

 

[Captain Sisko]

A toy rocket is launched at an angle of 30° above the horizontal with an initial velocity of 10 m/s. If the rocket reaches a height of 10 m, how far away does it land from the platform?

(cos 30° = 0.866, sin 30° = 0.500)

Simple question.. How can it possibly reach a height of 10m when the initial velocity is 10m/s here?

Using vf^2 = vi^2 + 2aY, (vf = 0 at the top)
we know that Y = Vi^2/2g = (10sin30)^2/2g = 25/2g = 1.25m.. So the height should have been 1.25m instead of 10m....

I didnt even have to use the height for this question, but still, why the heck did they say it reached 10m when it is not even possible?

It could be an alien on a world with a fraction of Earth's gravity. Use conservation of energy to find g:

m*g*h = .5 m v^2
g*10 = .5 * (5^2)

g = 1.25 m/sec^2

Then use this and your standard physics knowledge to find range.
v = vo + .5 a t^2
0 = 5 - .5*1.25*t^2
t until apex = sqrt 8 =~ 2.8
2t (when it lands) = 5.6 sec

5.6sec * 10cos30 = 49 m

ta da

ok so that was a weak attempt at humor. Aliens probably don't have toy rockets. or do they?

Captain Sisko

 

[brood910]

Hmmmm, it's probably a mistake on their part, but the original question mentions a platform. Did the rocket start at a height of 8.75m?

If it did, it will be a completely different story..
It started at h = 0.

 

[milski]

That's a sleazy way of telling you that g is not 9.8 m/s^2 in this case but I imagine something like this would be a fair game on the exam.

 

[brood910]

That's a sleazy way of telling you that g is not 9.8 m/s^2 in this case but I imagine something like this would be a fair game on the exam.

Nope.
The gravity is 9.8 for this question, as there's no way to get the answer for this question without it being 9.8.

The answer is ~8.7 which is possible to get with the equation 2VxVy/g.
Also, you could get it by doing this:

Tup = Voy/g = 10x0.5/10 = 0.5
0.5 x 2 = 1 for flight time
Range = 1 x Vx = 1 x 10(0.87) = 8.7

Also, if the gravity was not 9.8, the question should have told you about it since you cant solve for flight time, etc without it.

 

[milski]

Nope.
The gravity is 9.8 for this question, as there's no way to get the answer for this question without it being 9.8.

The answer is ~8.7 which is possible to get with the equation 2VxVy/g.
Also, you could get it by doing this:

Tup = Voy/g = 10x0.5/10 = 0.5
0.5 x 2 = 1 for flight time
Range = 1 x Vx = 1 x 10(0.87) = 8.7

Also, if the gravity was not 9.8, the question should have told you about it since you cant solve for flight time, etc without it.

You could solve for time & gravity from t*g=v0 and d=v0*t+g*t^2/2 but that gets 4 for the total flight time.

I don't see how they can consolidate 8.7 as an answer with all the information in the question.

 

[brood910]

You could solve for time & gravity from t*g=v0 and d=v0*t+g*t^2/2 but that gets 4 for the total flight time.

I don't see how they can consolidate 8.7 as an answer with all the information in the question.

That's why Im pointing out that the height cant be 10m.

 

[JLeBling]

This was a mistake plain and simple.

*Disappointment*