- #1
timetraveller123
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Homework Statement
What is the minimum initial velocity that has to be given to a stone in order to throw it across a sloped roof? The roof has width b, its two edges have heights a and c.
Homework Equations
The Attempt at a Solution
i decided to start simpler so
so i first looked at if was just a wall of a
then minimal velocity would be ## \sqrt{2gh}## with a little bit of forward velocity to get it over
if it was roof like this but both sides being height a and width b then the maximum height would have to occur somewhere over the middle of roof and the trajectory would have to touch the corners
i was doing something like this but i believe it should be simpler
##
v cos \theta t = x\\
v sin \theta t - \frac{g t^2}{2} = y \\
a = y\\
a = v sin \theta t - \frac{g t^2}{2} \\
##
the difference between the two times of this is
##
t_1 - t_2 = \frac{2}{g}\sqrt{v^2 sin\theta - a^2}\\
v cos\theta (t_1 - t_2) = b \\
v cos\theta \frac{2}{g}\sqrt{v^2 sin\theta - a^2} = b \\
##
i was hoping to express v as function theta from here and minimise with respect to theta but it seems overly complicated is there any other easier method