A golf ball is hit at an angle θ=45° to the horizontal with an initial speed v0. A vertical wall of height h=10m lies a distance d=20m away. Determine the minimum initial speed v0 required for the ball to clear the wall. Air resistance is negligible.
(I have a picture of a full explanation saved on my computer and I can show this or recreate using the whiteboard during interview if required.)
Physics: Newton's 2nd Law, 'suvat' equations.
Setting up problem:
1.Sketch problem.
2.Draw free-body diagram for golf ball.
3.Draw coordinate system.
Key Idea: Deal with horizontal and vertical forces independently to simplify problem.
Newton 2 in horizontal direction leads to expression horizontal distance x = v0tcosθ.
Newton 2 + 'suvat' leads to expression vertical distance y = v0tsinθ - (1/2)gt2.
Combine to eliminate t and obtain expression y = xtanθ - gx2/2v02cos2θ.
For minimum clearance of wall path crosses top of wall i.e. point (x=d, y=h). Sub in values for d=20m, h=10m, θ=45°, g=9.8ms-2. Final answer: v0 = 20ms-1 (2 sig. fig.)
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