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Projectile motion, finding initial velocity

1. The problem statement, all variables and given/known data
A rock is thrown from a 1 meter height with a 35 degrees angle with horizontal. At x=64 m, its height is y=29 m. Find it's initial velocity.


2. Relevant equations

[tex]x=x_{{0}}+v_{{{\it x0}}}t+ 0.5\,a_{{x}}{t}^{2}[/tex]
[tex]y=y_{{0}}+v_{{{\it y0}}}t+ 0.5\,a_{{y}}{t}^{2}[/tex]

3. The attempt at a solution
Let F = initial velocity
then Vx0 = F cos 35
Vy0 = F sin 35
[tex]x=x_{{0}}+v_{{{\it x0}}}t+ 0.5\,a_{{x}}{t}^{2}[/tex]
[tex]64=F\cos \left( 35 \right) t[/tex]
[tex]t=64\,{\frac {1}{F\cos \left( 35 \right) }}[/tex]

[tex]y=y_{{0}}+v_{{{\it y0}}}t+ 0.5\,a_{{y}}{t}^{2}[/tex]
[tex]29=1+64\,\tan \left( 35 \right) - 10035.20000\,{\frac {1}{{F}^{2}
\left( \cos \left( 35 \right) \right) ^{2}}}[/tex]
solving for F gives 102 m/s
the answer in the book is 42 m/s


sorry i am new to latex
 

alphysicist

Homework Helper
2,238
1
Hi fishingspree2,

1. The problem statement, all variables and given/known data
A rock is thrown from a 1 meter height with a 35 degrees angle with horizontal. At x=64 m, its height is y=29 m. Find it's initial velocity.


2. Relevant equations

[tex]x=x_{{0}}+v_{{{\it x0}}}t+ 0.5\,a_{{x}}{t}^{2}[/tex]
[tex]y=y_{{0}}+v_{{{\it y0}}}t+ 0.5\,a_{{y}}{t}^{2}[/tex]

3. The attempt at a solution
Let F = initial velocity
then Vx0 = F cos 35
Vy0 = F sin 35
[tex]x=x_{{0}}+v_{{{\it x0}}}t+ 0.5\,a_{{x}}{t}^{2}[/tex]
[tex]64=F\cos \left( 35 \right) t[/tex]
[tex]t=64\,{\frac {1}{F\cos \left( 35 \right) }}[/tex]

[tex]y=y_{{0}}+v_{{{\it y0}}}t+ 0.5\,a_{{y}}{t}^{2}[/tex]
[tex]29=1+64\,\tan \left( 35 \right) - 10035.20000\,{\frac {1}{{F}^{2}
\left( \cos \left( 35 \right) \right) ^{2}}}[/tex]
solving for F gives 102 m/s
the answer in the book is 42 m/s


sorry i am new to latex
The number 10035.2 in the above equation does not look right to me.
 
sorry the calculation was made using 20070.4 i don't know how the 10035.2 showed up

i get 102m/s using 20070.4 and it is not correct according to the book
 

alphysicist

Homework Helper
2,238
1
sorry the calculation was made using 20070.4 i don't know how the 10035.2 showed up

i get 102m/s using 20070.4 and it is not correct according to the book
I'm not getting 102m/s using 20070.4; can you show the details about how you get 102m/s?
 

Integral

Staff Emeritus
Science Advisor
Gold Member
7,184
54
I sorted out the constant. Thanks alphysicist.

It is usually a good idea to keep your expressions symbolic until the very end.

Show us how you are getting 102m/s.
 

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