Calculating Initial Speed for Successful Projectile Shot: Basketball Example

[Procrastinate]

A basketball player shoots a ball at an angle of 55^o into a hoop and lands in the net, which is 3.0m off the ground. Calculate the initial speed of the ball for this fould shot to be successful.

I did some vector integration and then isolated each of the components:

V_x= vcos55
V_y= vsin55 - gt
s_x= vcos55t
s_y= vsin55t - gt²/2 + 2.1

When

s_y= vsin55t - gt²/2 + 2.1 = 3
s_x= vcos55t = 4.3

However, even after some manipulating, there are two variables and I can't isolate any of them. Or maybe I am just missing something?

 

[housemartin]

Hello,

you got these two equations:
sy= vsin55t - gt2/2 + 2.1 = 3
sx= vcos55t = 4.3

can you from sx express t in terms of v and then put this in sy?

 

[pat666]

Hey, first off you need to approach the problem "more simply" some trig will hopefully give the horizontal distance to be 4.3m (what you've said, not right for the vales you've given it would be 2.1m. I am assuming typo in the given info) and then you have your component velocitys. From that s_i=4.3=vcos(55)t+0.5*0t^2 =v*cos(55)t and s_j=3=vsin(55)t+0.5*9.81t^2. you now have a system of simultaneous equations, solve them. (FYI i got t=0.8s and v = 9.4m/s) Please let me know if this was helpful(or even correct) thanks.