Finding the Optimal Angle for a Baseball to Return to its Release Point

[Larrytsai]

Homework Statement

A boy throws a ball upward with a speed of vo= 12m/s. The wind imparts a horizontal acceleration of 0.4m/s^2 to the left. At what angle theta must the ball be thrown so that it returns to the point of release. (assuming wind does not affect vertical motion.

Homework Equations

All physics equation

The Attempt at a Solution

I have written down all the formulas in the x and y directions, but it doesn't work out. I have also tried to look for what distance Vy=0 but i still end up having 2 unknowns.

 

[tiny-tim]

Hi Larrytsai!

(have a theta: θ and try using the X² tag just above the Reply box )

You should have only two unknowns, θ and t, so two equations should be enough.

Show us your full calculations, and then we can see what went wrong, and we'll know how to help!

 

[Larrytsai]

ok so what i have so far is,
for y:
y= (1/2 a t^2) + (Vo cosθ t)
(Vcosθ)^2 = (Vocosθ)^2 + 2ay

for x:
x= (1/2 a t^2) + (Vo sinθ t)
(Vsinθ)^2 = (Vosinθ)^2 + 2ax

so far how i see it is I am going to substitute my 2 x equations and my 2 y equations, then ill have 2 equations left to subtitute which are θ and time.

 

[tiny-tim]

ok so what i have so far is,
for y:
y= (1/2 a t^2) + (Vo cosθ t)
(Vcosθ)^2 = (Vocosθ)^2 + 2ay

for x:
x= (1/2 a t^2) + (Vo sinθ t)
(Vsinθ)^2 = (Vosinθ)^2 + 2ax

so far how i see it is I am going to substitute my 2 x equations and my 2 y equations, then ill have 2 equations left to subtitute which are θ and time.

(hmm … the second and fourth equations are just V = V₀ … that doesn't help much)

What's the difficulty?

Put all the numbers in, including x = y = 0, and what do you get?

 

[Larrytsai]

ohh ok, i got the answer, thnx so much, but I am a little confused as to why x is 0, I am thinking that when the height and horizontal distance is 0 , the ball has landed back in the boys hand, therefore the time elapsed is the same so we can subsitute for time?

btw thanks alot

 

[tiny-tim]

Hi Larrytsai!

Yes, you're getting confused.

When the ball returns to the hand, both x and y are 0, and the time elapsed is t (say).

So the same t appears in both the equation for x and the equation for y.

 

[C A S A]

What substitutions were made?