Two hard physics questions . Help PLEASE!!
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Two hard physics questions . Help PLEASE!!

[From: ] [author: ] [Date: 11-11-07] [Hit: ]
the first one is a thrown at an angle of 70 degrees with respect to the horizontal. At what angle should the second snowball be thrown to arrive at the same point as the first? How many seconds later should the second snowball be thrown after the first to arrive at the same time?thanks for your help-First find how long it will take for the first snowball to land.d = d₀ + v₀t + 0.0 = 0 + 25*sin(70)*t + 0.......
one strategy in a snowball fight is to throw a snowball at a high angle over lever ground. while your opponent is watching the first one, you throw a second snowball at a low angle timed to arrive before or at the same time as the first one. assume both snowballs are thrown with a speed of 25 m/s. the first one is a thrown at an angle of 70 degrees with respect to the horizontal. At what angle should the second snowball be thrown to arrive at the same point as the first? How many seconds later should the second snowball be thrown after the first to arrive at the same time?

thanks for your help

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First find how long it will take for the first snowball to land. This is for the y-direction only
d = d₀ + v₀t + 0.5at²
0 = 0 + 25*sin(70)*t + 0.5(-9.81)*t²
t = 4.78946 s

Then find how far the ball travels in the x-direction
d = d₀ + v₀t + 0.5at²
d = 0 + 25*cos(70)*4.78947 + 0
d = 40.9524 m

Now, write the x and y equations for the second ball. Since t are the same for both. Solve for t in one of the equations and plug it in for the other.
For the x-direction
d = d₀ + v₀t + 0.5at²
40.9524 = 0 + 25*cosθ*t + 0
t = 40.9524 / 25*cosθ

Do the same for the y-direction.
d = d₀ + v₀t + 0.5at²
0 = 0 + 25*sin(θ)*t + 0.5(-9.81)*t²

Now plug in t from your x equation to solve for θ.
0 = 25*sin(θ)*[40.9524 / 25*cosθ] + 0.5(-9.81)*[40.9524 / 25*cosθ]²
0 = 40.9524*tan(θ) - 13.148/cos²θ
0.3287 = sin(θ)*cosθ
0.3287 = 0.5sin(2θ)
θ = 19.975º

Now to find how long it will take to arrive if thrown at 19.975º.
t = 40.9524 / 25*cosθ
t = 40.9524 / 25*cos(19.975)
t = 1.7429 s

t₁ - t₂ = 4.78946 - 1.7429 = 3.04 s

So the second ball should be thrown at roughly 19.975º to arrive at the same point and it should be thrown 3.0465 seconds later to arrive at the same time. Good question.
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