Need Help With Physics Problem!

[User2983]

I have been working on this physics problem and I have some problems. The original question is:

How do you check if a basketball shot with 13.5 m/s initial velocity at a 55 degree angle and the ball is being launched 5.5 ft(or 1.68 meters) off the ground goes into a 10 ft(3.05 meters) hoop?

 

I know it goes in the hoop but I can't prove it.

 

dy=viy*t + 1/2*ay*t*t

3.0488 = (13.5*sin55*2.0663)+(.5*-9.8*2.0663^2)<--- when you calculate, they don't equal each other

 

that is the work I have but as you can see, it's not that good.

 

Any help would be appreciated. :naughty:

[sanctus]

How did you find t=2.0663. I've got a solution in mind, but as you didn't write everything ...

 

And hoop is at height 3.05 or at a distance 3.05? If it at height you just have to show that there is a time>0 where y(t)=3.05

[User2983]

How did you find t=2.0663. I've got a solution in mind, but as you didn't write everything ...

 

And hoop is at height 3.05 or at a distance 3.05? If it at height you just have to show that there is a time>0 where y(t)=3.05

 

 

I never put in that the distance from the person to the hoop is 16 meters. That's where i got

16=13.5 cos55 * t and i just solved for t. And the hoop is at a height of 3.05 meters

[niviene]

Can you subtract the height of the launch (1.68 meters) from the height of the hoop (1.3688 meters) and then graph it and see where y is when x = 16? Can you post what your variables all stand for?

[User2983]

Can you subtract the height of the launch (1.68 meters) from the height of the hoop (1.3688 meters) and then graph it and see where y is when x = 16? Can you post what your variables all stand for?

 

Dy=Distance in the y direction(meters)

T=time

Viy= Initial velocity in y direction(initial velocity * sin theta)(meters/seconds)

Ay= acceleratuon in the y direction....gravity(meters/second^2)

 

and the height of the hoop is 3.05 meters

[Jay-qu]

ok, the thing that links horizontal and vertical motion when doing projectile motion questions is time. so we first have to calculate time in a vertical sense.

- use the equation: s = ut + 1/2 a t^2 ; where s = displacement(m), u = initial virtical velocity (m/s), t = time (sec), a = acceleration(m/s/s).

NOTE: if you call up +ve then your a value will be -9.8m/s/s

sub in all those values you had... -> i got a value of 2.13sec

so now that we now that the ball spends 2.13 seconds in the air between launch and the height of the hoop, i would use v = s / t , v = 13.5cos(55) m/s and t = 2.13 s

making s = 3.64 m

now you havent specified a distance horizontally to the hoop, was this part of the question? if the hoop is about 3.64 m away then it would fall though...

[niviene]

I guess I'm a little confused about your condition for success.... you don't mention the size of the ball or the hoop... the question is poorly written, really... does the ball have to go cleanly through the hoop? Is the hoop an object with a radius greater than that of the ball?

 

I'm guessing they're just kind of dumbing down the question...split the two vectors - the angle of inclination is 13.5 degrees.

 

13.5 * sin 55 (y vector)

13.5 * cos 55 (x vector)

 

multiply x velocity by the time you have, and see where it puts you. if the ball is there at 16 meters, you have proven your equation. I assume you have a little leeway, but it seems like more info that's needed is left out....

[User2983]

I guess I'm a little confused about your condition for success.... you don't mention the size of the ball or the hoop... the question is poorly written, really... does the ball have to go cleanly through the hoop? Is the hoop an object with a radius greater than that of the ball?

 

I'm guessing they're just kind of dumbing down the question...split the two vectors - the angle of inclination is 13.5 degrees.

 

13.5 * sin 55 (y vector)

13.5 * cos 55 (x vector)

 

multiply x velocity by the time you have, and see where it puts you. if the ball is there at 16 meters, you have proven your equation. I assume you have a little leeway, but it seems like more info that's needed is left out....

 

yeah the problem included some error. If the basketball is less than half a meter +/- from the height of the hoop, it was considered a made jump shot. I wish this was included before I bothered you guys about the equations not working. Thanks for all of the help you guys gave me ;)