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Mathematics-Online problems:

Problem of the week

During a soccer game the referee blew a penalty. Unfortunately, the penalty taker hit the middle of the crossbar and did not score.


At which velocity $ v$ and angle $ \alpha$ did the player shoot the ball from the penalty point when he hit the crossbar (height 2.50m) horizontally?

After which flying time $ t$ and at which velocity $ v_H$ does the ball hit the crossbar?

Hint: Use the simplified equations of motion

$\displaystyle x(t)$ $\displaystyle =$ $\displaystyle vt\cos\alpha$  
$\displaystyle y(t)$ $\displaystyle =$ $\displaystyle vt\sin\alpha -\frac{1}{2}\,gt^2\,,\quad \
g=10\,\frac{\rm {m}}{\rm {s}^2}\,.$  


$ v$ $ =$ $ \frac{\rm {m}}{\rm {s}}$              
$ \tan\alpha$ $ =$              
$ t$ $ =$ s              
$ v_H$ $ =$ $ \frac{\rm {m}}{\rm {s}}$              

(The results should be correct to four decimal places.)


[solution to the problem of the previous week]