# Projectile motion snowball problem

1. Nov 26, 2007

### guitarguybri

1. The problem statement, all variables and given/known data

One child is trying to hide from another who is throwing snowballs. The first child hides by crouching behind a 2.5 m high fence that is 4 m from the other child's snow fort. The second child tries to hit the hiding child by lobbing snowballs over the fence as shown in the figure. If the maximum speed with which the second child can throw a snowball is 10 m/s, what is the closest distance to the backside of the fence that he can get a snowball to land? (Assume the snowball is released at a height equal to that of the back of the fence.)

vi = 10m/s
delta_y= 2.5m
delta_x = x + 4m
g = 9.8 m/s2
yf = 0 m

t - ?
xf - ?

2. Relevant equations

yf = vyi*t - .5*g*t^2 --> vi*(sin theta)*t - .5*g*t^2
xf = vxi*t --> vi*(cos theta)*t

t = xf / (vi*cos theta)

after much algebra and trig substitutions (I got rid of t in the yf equation).

0 = ((g*(xf)^2)*(tan theta)^2)/(2*(vi)^2) -xf*tan theta + (g*(xf)^2)/(2*(vi)^2) + yf

(-b +/- sqrt((b)^2 - 4ac)) / 2a -- quadratic formula

3. The attempt at a solution

I want to use the second to last equation I listed. I want to use the quadratic formula to solve for tan theta. Then I can take the inverse tangent and get the angle. Then I can use kinematic equations to find the distance that I want. Which will be 4m + x. But I have too many unkowns and not enough equations. I want to know how to find out what xf is. I think I can handle it after that. I just need to be able to use the quadratic formula to find my angle theta. Thanks!

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