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Introductory Physics Homework Help
Projectile Motion on Inclined Surface Question
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[QUOTE="ltkach2015, post: 5198862, member: 520445"] [h2]Homework Statement [/h2] Water is sprayed at an angle of 90° from the slope at 20m/s. Determine the range R. PLEASE SEE ATTACHMENT[h2]Homework Equations[/h2] [/B] Kinematic Equations: acceleration: [B]A = [/B]0[B]i +[/B]g[B](-j) + [/B]0[B]k; [/B] velocity: [B]dV/dt = A;[/B] position: [B]dR/dt = V;[/B] Origin set at the point spout of water. Angle of the plane: θ = atand(3/4) = 36.869° Magnitude of acceleration: g = 9.81; Initial Conditions Velocity: Vb(t=0) = 10; => [B]Vb(t=0) = [/B]Vb*cosd(90-θ)*[B](-i)[/B] + Vb*sind(90-θ*[B](-j)[/B] + 0*[B](-k)[/B] Position: [B]Rb(t=0) = [/B]0*[B](i) + [/B]0*[B](j) [/B]+ 0*[B](k)[/B][h2]The Attempt at a Solution[/h2][U]1) integrate acceleration: [/U][B]A = [[/B]0; -g ;0[B]][/B] = [B]dVb/dt[/B] [B]∫dVb = ∫ [[/B]0; -g; 0[B]][/B] dt => [B]Vb(t) = [/B]c1*[B](i) [/B]+ (-g*t + c2)*[B](-j) [/B]+ c3*[B](k); [/B]impose initial conditions: [B]Vb(t=0) = [/B]Vb*cosd(90-θ)*[B](-i)[/B] + Vb*sind(90-θ)*[B](-j)[/B] + 0*[B](-k)[/B] => c1 = Vb*cosd(90-θ); c2 = Vb*sind(90-θ); c3 = 0; [U]2) integrate velocity:[/U] ∫[B]dR = [/B]∫[B][B]Vb(t)dt = Vb(t) = [-[/B][/B]Vb*cosd(90-θ); g*t + Vb*sind(90-θ); 0[B]]dt;[/B] => [B]R(t) =[/B] (Vb*cosd(90-θ)*t + c4)[B]*[B](i) [/B]+ [/B](-g/2*t^2 + Vb*sind(90-θ)*t + c5)[B]*[B](j) [/B]+ [/B]c6[B]*[B](k) [/B][/B] impose initial conditions: [B]Rb(t=0) = [/B]0*[B](i) + [/B]0*[B](j) [/B]+ 0*[B](k)[/B] => c4 = 0; c5 = 0; c6 = 0; [U]3) List of Derived Equations: [/U] [B]R(t) =[/B] (-Vb*cosd(90-θ)*t )[B]*[B](i) [/B]+ [/B](-g/2*t^2 + Vb*sind(90-θ)*t )[B]*[B](j) [/B]+ [/B]0[B]*[B](k)[/B][/B] [B]Vb(t) = [/B]([B]-[/B]Vb*cosd(90-θ))[B]*(i) [/B] + (-g*t + Vb*sind(90-θ))[B]*(j)[/B] + 0*[B](k)[/B] [U]4) Equation of Inclined Plane:[/U] f(x) = 3/4*x [U] 5) Parametrize the position function:[/U] x(t) = (-Vb*cosd(90-θ)*t ) => t = x(t)/(Vb*cosd(90-θ) y(x(t)) = Vbsind(90-θ)*{x(t)/(Vb*cosd(90-θ))} - g/2*({x(t)/(Vb*cosd(90-θ))}^2 [U]6) Find the Intersection of the two plane curves. 7) Use magnitude of x and y to find Range: (probably didn't say that correctly) [/U] Range = sqrt( xi^2 + yi^2)I would appreciate all the help I can get. Thank you. [/QUOTE]
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Projectile Motion on Inclined Surface Question
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