# Two dimensional motion

I got stuck in problem which states: "A basket ball player 2m high wants to make a goal from 10m from basket. If he shoots the ball at a 45 degree angle, at what initial speed must he throw the basketball. Height of basket is 3.05m." Please help.

CWatters
Homework Helper
Gold Member
Sounds like homework so the mods might move this to the homework section. You should also use the homework template which has sections to fill in. Saves us time repeating stuff you already know.

Hint: Write equations for the horizontal and vertical motion. Then realise that the time at which the ball goes through the hoop is the same in both equations. Should give you enough equations and known variables to allow you to solve for the launch velocity. Perhaps start by subtracting 2m from all the heights so that the ball is launched from the ground towards a hoop at height 1.05m high.

Sounds like homework so the mods might move this to the homework section. You should also use the homework template which has sections to fill in. Saves us time repeating stuff you already know.

Hint: Write equations for the horizontal and vertical motion. Then realise that the time at which the ball goes through the hoop is the same in both equations. Should give you enough equations and known variables to allow you to solve for the launch velocity. Perhaps start by subtracting 2m from all the heights so that the ball is launched from the ground towards a hoop at height 1.05m high.
I have tried but it gives quadratic equations which make solution even more complicated.

haruspex
Homework Helper
Gold Member
I have tried but it gives quadratic equations which make solution even more complicated.
More complicated than what? Than no solution at all?
Please post your working as far as you can get. Since, as CW pointed out, you have to use common time to connect the horizontal and vertical motions, solving a quadratic will be unavoidable.

CWatters
Homework Helper
Gold Member
Quite frequently there are two solutions to projectile problems. For example if you throw a ball there will be two occasions when it's at height X, once on the way up and once on the way down. So perhaps not surprising there is a quadratic to be solved sometimes.

Perhaps use..

More complicated than what? Than no solution at all?
Please post your working as far as you can get. Since, as CW pointed out, you have to use common time to connect the horizontal and vertical motions, solving a quadratic will be unavoidable.
I have derived equations for common time
Quite frequently there are two solutions to projectile problems. For example if you throw a ball there will be two occasions when it's at height X, once on the way up and once on the way down. So perhaps not surprising there is a quadratic to be solved sometimes.

Perhaps use..
I have an attempt in solving it. Please guide me how to carry on further.See the figure

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CWatters
Homework Helper
Gold Member
Can you show us your working to get to the equation in that image.

Can you show us your working to get to the equation in that image.
What should I equate time to? I have equated it equal to " total time - time to reach 10m distance" but it gives equation of degree 4.

haruspex