Calc 3-Throwing a baseball at 30 degrees from horizontal
- Thread starter riverjib
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Re: Calc 3-Throwing a baseball
\(\displaystyle x=(V_{0}cos(\theta)t\)
\(\displaystyle y=s_{0}+(V_{0}sin(\theta))t-\frac{1}{2}gt^{2}\)
First, we can solve for t by setting y=0 in the last equation and solving for t.
\(\displaystyle 0=32+32sin(30)t-16t^{2}\)
Solve this for t to find the time 'til it hits the ground. Then sub that t value into the formula for x to find how far away it lands,
\(\displaystyle x=(V_{0}cos(\theta)t\)
\(\displaystyle y=s_{0}+(V_{0}sin(\theta))t-\frac{1}{2}gt^{2}\)
First, we can solve for t by setting y=0 in the last equation and solving for t.
\(\displaystyle 0=32+32sin(30)t-16t^{2}\)
Solve this for t to find the time 'til it hits the ground. Then sub that t value into the formula for x to find how far away it lands,
Dr. Flim-Flam
Junior Member
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- Oct 10, 2007
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- 108
The ball will remain in the air for a total of
t =[vsin? + ?(v²sin²?+2gh)]/g where v=32, g=32,h=32 and ?=?/6. Hence t = 2 sec.
The ball will go a horizontal distance of
d =[ (v²cos?)/g] [sin?+?(sin²?+2gh/v²)]. Hence d = 32?3 feet.
t =[vsin? + ?(v²sin²?+2gh)]/g where v=32, g=32,h=32 and ?=?/6. Hence t = 2 sec.
The ball will go a horizontal distance of
d =[ (v²cos?)/g] [sin?+?(sin²?+2gh/v²)]. Hence d = 32?3 feet.
A baseball is thrown from the stands 32ft above the field at 30 degrees from horizontal. When and how far away will it land if the initial speed is 32ft/sec?
Vv = 32sinµ = 16
Vh = 32cosµ 27.7128
1--From Vf = Vo - gt, o = 16 - 32t1 making t1 = .5 sec.
2--From h = Vvt1 - 32t1^2/2, h1 = 16(.5) - 16(.5^2) = 4 ft.
3--From h2 = Vvt2 + 16t2^2, 36 = 0 + 16(t2^2 making t2 = 1.5sec.
4--WIth T = .5 + 1.5 = 2 sec., d = 2(32)cosµ = 55.42 ft.
Vv = 32sinµ = 16
Vh = 32cosµ 27.7128
1--From Vf = Vo - gt, o = 16 - 32t1 making t1 = .5 sec.
2--From h = Vvt1 - 32t1^2/2, h1 = 16(.5) - 16(.5^2) = 4 ft.
3--From h2 = Vvt2 + 16t2^2, 36 = 0 + 16(t2^2 making t2 = 1.5sec.
4--WIth T = .5 + 1.5 = 2 sec., d = 2(32)cosµ = 55.42 ft.
Dr. Flim-Flam
Junior Member
- Joined
- Oct 10, 2007
- Messages
- 108
Note: If you have a plethora of problems like this, make up a template or two
(I gave you two equations) and instead of having to do a lot of grunt work, just plug in your
values to the appropriate template, and walla, you have solve the problem without the
usual expenditure of time.
(I gave you two equations) and instead of having to do a lot of grunt work, just plug in your
values to the appropriate template, and walla, you have solve the problem without the
usual expenditure of time.
D
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Re: Calc 3-Throwing a baseball
You have 2-D problem - If the ball was swinging in/out of the strike zone then it would be a 3-D problem.
However, 3-D problems are similar - write those equations in each individual dimensions - and then add those vectorially - simple (tongue firmly planted in the cheek).
riverjib said:
You have 2-D problem - If the ball was swinging in/out of the strike zone then it would be a 3-D problem.
However, 3-D problems are similar - write those equations in each individual dimensions - and then add those vectorially - simple (tongue firmly planted in the cheek).