Projectile motion 2-d kinematics

AI Thread Summary
The discussion revolves around a projectile motion problem from Cutnell & Johnson's textbook, involving students launching water balloons between two dorms. The first balloon, launched from Jackson dorm, hits Walton dorm after 2 seconds, requiring the calculation of its initial velocity angle, which is determined to be 24.0 degrees. The initial speed for this balloon is calculated to be 19.2 m/s. A second balloon, launched at the same angle, is reported to have an initial speed of 28.9 m/s. Participants express appreciation for the assistance in verifying their calculations, highlighting the challenges of confirming answers for even-numbered problems in their coursework.
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This is an even problem from Cutnell & Johnson 8 edition. Can anyone verify if it is correct?

In the annual battle of the dorms, students gather on the roofs of Jackson and Walton dorms to launch water balloons at each other with slingshots. The horizontal distance between the buildings is 35.0 m, and the heights of the Jackson and Walton buildings are, respectively, 15.0 m and 22.0 m. Ignore air resistance.

(a) The first balloon launched by the Jackson team hits Walton dorm 2.0 s after launch, striking it halfway between the ground and the roof. Find the direction of the balloon's initial velocity. Give your answer as an angle measured above the horizontal.

(b) A second balloon launched at the same angle hits the edge of Walton's roof. Find the initial speed of this second balloon.

MY WORK FOR PART A

t = 2 seconds
x = 35 meters
y = -4 meters

Vox = x/t = 35/2
Vox = 17.5 m/s
Vox = VocosƟ
17.5 = VocosƟ
Vo = 17.5/cosƟ

Voy = Vo + at

y = Voyt + 0.5at2 = -VosinƟ -4.9t2
-4 = (17.5/cosƟ)sinƟt -4.9t2 <----plug in t = 2
-4 = (17.5)(2)tanƟ - (4.9)(4)
Ɵ = 24.0 degrees

Vo = 17.5/cosƟ
Vo = 17.5/cosƟ = 19.2 m/s

ahh i forgot to do part B...But the answer is 28.9 m/s for part B?
 
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jehan4141 said:
This is an even problem from Cutnell & Johnson 8 edition. Can anyone verify if it is correct?

In the annual battle of the dorms, students gather on the roofs of Jackson and Walton dorms to launch water balloons at each other with slingshots. The horizontal distance between the buildings is 35.0 m, and the heights of the Jackson and Walton buildings are, respectively, 15.0 m and 22.0 m. Ignore air resistance.

(a) The first balloon launched by the Jackson team hits Walton dorm 2.0 s after launch, striking it halfway between the ground and the roof. Find the direction of the balloon's initial velocity. Give your answer as an angle measured above the horizontal.

(b) A second balloon launched at the same angle hits the edge of Walton's roof. Find the initial speed of this second balloon.

MY WORK FOR PART A

t = 2 seconds
x = 35 meters
y = -4 meters

Vox = x/t = 35/2
Vox = 17.5 m/s
Vox = VocosƟ
17.5 = VocosƟ
Vo = 17.5/cosƟ

Voy = Vo + at

y = Voyt + 0.5at2 = -VosinƟ -4.9t2
-4 = (17.5/cosƟ)sinƟt -4.9t2 <----plug in t = 2
-4 = (17.5)(2)tanƟ - (4.9)(4)
Ɵ = 24.0 degrees

Vo = 17.5/cosƟ
Vo = 17.5/cosƟ = 19.2 m/s

ahh i forgot to do part B...But the answer is 28.9 m/s for part B?

Nice method of calculation!
 
WOOHOO! Thank you! I love this site...My teacher refuses to give us the answers for even problems, even right before the quiz! How are we supposed to know if we are doing it right :(
 
jehan4141 said:
WOOHOO! Thank you! I love this site...My teacher refuses to give us the answers for even problems, even right before the quiz! How are we supposed to know if we are doing it right :(

If you think you have the right answer, you are most probably right. If you are not sure whether you are right, you are quite possibly wrong. CONFIDENCE! - backed up by sound preparation.
 

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