- #1
vande060
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A golfer drives a ball horizontally with
initial velocity v = (50m/s , 0) from a tee at the
origin, down a 20deg below-horizontal slope as
illustrated above.
A. How far from the tee measured along
the slope does the ball land on the slope?
B. With what speed does it land?
a link to the page in the book with the problem: http://s861.photobucket.com/albums/ab174/alkaline262/?action=view¤t=chapter2question.jpg
x(t) = x0 + v0x*t + 1/2*a*t^2
y(t) = y0 + v0y*t + 1/2*a*t^2
x(t) = v0*t
y(t) = -1/2*g*t^2
solving x(t) for t:
t = (x/v0)
inserting in y equation fro trajectory:
y(x) = -1/2*g*(x/v0)^2
i will call the projectile range R, as it would be along the x axis. to compensate for the slope of the hill i will now substitute into the trajectory equation:
R*sin(θ) = -1/2*g*([R^2*cos(θ)^2]/v0^2)
solving for R i get (sin(θ)*-2*v0^2*)/(cos^2*g) = R
inserting v0=50 and θ=-20deg i get the range to be 197
my prof says the range is 185, which i would have gotten i the cos of the denominator was not squared, where is my error here?
I am still working on the second part, but need to clear this up first. Any help would be greatly appreciated
initial velocity v = (50m/s , 0) from a tee at the
origin, down a 20deg below-horizontal slope as
illustrated above.
A. How far from the tee measured along
the slope does the ball land on the slope?
B. With what speed does it land?
a link to the page in the book with the problem: http://s861.photobucket.com/albums/ab174/alkaline262/?action=view¤t=chapter2question.jpg
x(t) = x0 + v0x*t + 1/2*a*t^2
y(t) = y0 + v0y*t + 1/2*a*t^2
x(t) = v0*t
y(t) = -1/2*g*t^2
solving x(t) for t:
t = (x/v0)
inserting in y equation fro trajectory:
y(x) = -1/2*g*(x/v0)^2
i will call the projectile range R, as it would be along the x axis. to compensate for the slope of the hill i will now substitute into the trajectory equation:
R*sin(θ) = -1/2*g*([R^2*cos(θ)^2]/v0^2)
solving for R i get (sin(θ)*-2*v0^2*)/(cos^2*g) = R
inserting v0=50 and θ=-20deg i get the range to be 197
my prof says the range is 185, which i would have gotten i the cos of the denominator was not squared, where is my error here?
I am still working on the second part, but need to clear this up first. Any help would be greatly appreciated