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Physics Problem of the Week for Sep 15 2014

Basketball free throw

You want to make a free throw in basketball. You are standing 4.6 m from the basket, which is 3 m high. You throw the ball at an angle of $30^\circ$, from a height of 1.5 m. With what speed do you need to throw the ball in order to make it into the basket with "nothing but net?"

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Steps accepted thus far

  • At 30 degrees, I would start by finding the x and y components of the ball's velocity.

  • Here, $v_x=v\cos30$ and $v_y=v\sin30$. So the ball's initial speed to the right is $v_x$ and the initial speed up is $v_y$.

  • Let's now see how long the ball is in the air: it starts 1.5 m high and needs to end up 3 m high, given that is is launched vertically at vsin30.

  • The time in the air is then $3=1.5+v\sin30t-\frac{1}{2}gt^2$. We need to solve this for $t$.

  • We also know that in the same time $t$, the ball should go horizontally 4.6 m, or $4.6=0+vcos30t$.

  • These are 2 equations and two unknowns in $v$ and $t$. I used Wolfram Alpha to solve them and got $v=7.7$ m/s.

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