Basketball player shoots a ball, find angle, parametrics

[Pi Face]

Homework Statement

A basketball player shoots a ball with a speed off 25 ft/sec from a point 15 ft horizontally away from the center of the basket. The basket is 10ft away above the the floor and the player releases the ball from a height of 8ft. At what angle should the player shoot the ball?

Homework Equations

Actually, this is one of my calc problems, but it seems physics-y enough to be posted here. I'm supposed to use parametrics to solve it.

x(t)=x₀+h₀t
y(t)= -(1/2)gt²+v₀t+y₀
h₀=s₀cos$$\theta$$
v₀=s₀sin$$\theta$$

The Attempt at a Solution

I don't feel like typing all these sub/superscripts, but I worked with the y(t) function, set v₀ to 25 and y₀ to 8 and got 0.0846 and 1.478 for values of t. But then I realizes that v₀ was supposed to be s₀cos$$\theta$$, which means I have both t and theta in the equation. How would I solve for either variable? Thanks.

 

[rl.bhat]

x(t) = vo*coaθ*t, where vo is the velocity of projection.
Find t = ...(1)
y(t) = yo + vo*sinθ*t - 0.5*g*t^2.
Substitute the appropriate values and find vo.

 

[Pi Face]

Uh...
how do I solve for t in x(t) = vo*cosθ*t?
am I supposed to get a number? i get t= x/(vo*cosθ)

 

[rl.bhat]

Uh...
how do I solve for t in x(t) = vo*cosθ*t?
am I supposed to get a number? i get t= x/(vo*cosθ)

Yes.

 

[Pi Face]

yes to a number or yes I solved it right?

anyways, so then I substitute x/(vo*cosθ) for t in the y(t) equation? fun >.>

 

[rl.bhat]

yes to a number or yes I solved it right?

anyways, so then I substitute x/(vo*cosθ) for t in the y(t) equation? fun >.>

Expression for t is correct.
Substitute in y(t) and solve for vo.

 

[Pi Face]

but what's theta? I have two unknowns, vo and theta.

 

[rl.bhat]

but what's theta? I have two unknowns, vo and theta.

Vo = 25 ft/s.

 

[Pi Face]

can't believe i missed that. I am all set now. thanks!