Mechanics
FREE SOLUTION - A 2.00-m-tall basketball player is standing on the floor 10.0 m from the basket
A 2.00-m-tall basketball player is standing on the floor 10.0 m from the basket, as in Figure. If he shoots the ball at a 40.0Њ angle with the horizontal, at what initial speed must he throw the basketball so that it goes through the hoop without striking the backboard? The height of the basket is 3.05 m.
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhAKHMyn5akMqqc3BARLP47BEtdPzPBC91xnKG2-2bIoiUQsyjnLBotfZIDdVjsxcEbuK-w4kqnW9NjY05zkkgJa5k1p3mQPFGHdX8cTPdX8V8zDstrOOFiMSSWlpf94rXdo7gd5s-tznA/s320/A-2-m-tall-basketball-player-is-standing.png)
Let's get started to solve this problem, our first goal here is find the movement equations for each axes. But, before write any equation, it's too recommended draw a simple picture of our problem, something like this:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiJiYYYoyhdWnmoRW6IcQsDT8GnUZwXdRC02IIMaD7QFg7cprpKqyl7Ja1rJOQXksO2taGtjOeg1mL8y1cpRzDFEm50QI8Eig-mXyNMxkcIwW0_nRDUYBf0xoP0gL1OYRiIy4EapUcPwjU/s320/basic-problem-picture.jpg)
Now it's time to write the movement equations, for y-axis we have a parabolic motion and for x-axis a constant speed motion like this:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgZrBubYwwWzprol0f6MFUIEzUh7aTNodbVkOr_iCYcOmVGWuLmdJaTE7ZG8R8YgTVp8ScsBeodXA8ZCgF43TnlsYHz6JmwUJWmZrfOiM-8Tx0e4G_V0bH5dy6i-OkNFJJpoop0S6hBQok/s400/parabolic-equations.jpg)
Well, only left solve some algebraic issues where the unknown variable is the initial speed, working on !
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhnlqLZPesNZ4jlpc5ZjhJDThpr7Z1VjKokUN0ZEr_pPk2GLnJc3UV1FErDe3XXWcTrew-WFMAwCiMDYIiBUO_w_T6OOoCzS-JtKZZ-JQ7SHzMWIt_1HKsiV_5Xs1XKdnm7yu0zSCZ_lXo/s400/solving-parabolic-problem.jpg)
Replace the values for each variable x_f, y_o, y_f and theta to get the result.
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg3Pre56t0TR9RJg5qDFDZ-MhzuyXZRSAL7VykX2WsKSU5TkzXKki5UxdXURCvMCQ-JBGfefHkpAFOAJ3kKcLUhsVlNHqX9hCZG72drjnXRThOT8VC41eAWPEVKimH9JLOps5yYSKMEzvk/s400/initial-speed-value.jpg)
Nice! remember that you need be congruent when solve a physics problem, a magnitude analysis is necessary to be sure that our answer is correct, so, if you don't obtain m/s after the magnitude analysis, the bad new is that a complete revision of your algebra is needed.
This is all for this post, if you like our work... share it with your friends! see ya! and remember physics it's easy very easy... ;)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhAKHMyn5akMqqc3BARLP47BEtdPzPBC91xnKG2-2bIoiUQsyjnLBotfZIDdVjsxcEbuK-w4kqnW9NjY05zkkgJa5k1p3mQPFGHdX8cTPdX8V8zDstrOOFiMSSWlpf94rXdo7gd5s-tznA/s320/A-2-m-tall-basketball-player-is-standing.png)
A 2.00-m-tall basketball player
Let's get started to solve this problem, our first goal here is find the movement equations for each axes. But, before write any equation, it's too recommended draw a simple picture of our problem, something like this:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiJiYYYoyhdWnmoRW6IcQsDT8GnUZwXdRC02IIMaD7QFg7cprpKqyl7Ja1rJOQXksO2taGtjOeg1mL8y1cpRzDFEm50QI8Eig-mXyNMxkcIwW0_nRDUYBf0xoP0gL1OYRiIy4EapUcPwjU/s320/basic-problem-picture.jpg)
Now it's time to write the movement equations, for y-axis we have a parabolic motion and for x-axis a constant speed motion like this:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgZrBubYwwWzprol0f6MFUIEzUh7aTNodbVkOr_iCYcOmVGWuLmdJaTE7ZG8R8YgTVp8ScsBeodXA8ZCgF43TnlsYHz6JmwUJWmZrfOiM-8Tx0e4G_V0bH5dy6i-OkNFJJpoop0S6hBQok/s400/parabolic-equations.jpg)
Well, only left solve some algebraic issues where the unknown variable is the initial speed, working on !
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhnlqLZPesNZ4jlpc5ZjhJDThpr7Z1VjKokUN0ZEr_pPk2GLnJc3UV1FErDe3XXWcTrew-WFMAwCiMDYIiBUO_w_T6OOoCzS-JtKZZ-JQ7SHzMWIt_1HKsiV_5Xs1XKdnm7yu0zSCZ_lXo/s400/solving-parabolic-problem.jpg)
Replace the values for each variable x_f, y_o, y_f and theta to get the result.
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg3Pre56t0TR9RJg5qDFDZ-MhzuyXZRSAL7VykX2WsKSU5TkzXKki5UxdXURCvMCQ-JBGfefHkpAFOAJ3kKcLUhsVlNHqX9hCZG72drjnXRThOT8VC41eAWPEVKimH9JLOps5yYSKMEzvk/s400/initial-speed-value.jpg)
Nice! remember that you need be congruent when solve a physics problem, a magnitude analysis is necessary to be sure that our answer is correct, so, if you don't obtain m/s after the magnitude analysis, the bad new is that a complete revision of your algebra is needed.
This is all for this post, if you like our work... share it with your friends! see ya! and remember physics it's easy very easy... ;)