You are playing an innovative fortress defence game. You build a 4.0 m-high fort
ID: 2134878 • Letter: Y
Question
You are playing an innovative fortress defence game. You build a 4.0 m-high fortress out of wood and cover the front wall with a thin layer of playdough. Your opponents build their fortress 10 m from yours and mount a home-built cannon at its edge, 4.0 m above the ground. Their cannon fires baseballs with a speed of 9.9 m/s. They fire a baseball at your fortress at an angle of 45
You are playing an innovative fortress defence game. You build a 4.0 m-high fortress out of wood and cover the front wall with a thin layer of playdough. Your opponents build their fortress 10 m from yours and mount a home-built cannon at its edge, 4.0 m above the ground. Their cannon fires baseballs with a speed of 9.9 m/s. They fire a baseball at your fortress at an angle of 45degree above the horizontal. The opponents score points with every mark their baseball leaves on your playdough. You have a defensive cannon that shoots golf balls at a speed of 29.8 m/s. If your cannon fires from ground level the exact instant their cannon fires, at what angle must you fire your golf ball to hit the incoming baseball? (Assume that the base of your fortress and your cannon is at the origin of the x- and y-axes. Your cannon points in the +x- and +y-direction which is to the right and up, respectively.)Explanation / Answer
in vertical :
29.8sinA x t - 9.8t^2 /2 = 9.9sin45 x t - 9.8t^2 /2 + 4
29.8sinA t = 7t + 4
in horizontal :
(29.8cosA + 9.9 cos45)t = 10
(29.8cosA + 7)t = 10
t = 10 / (29.8cosA + 7)
put the velue of t
29.8sinA x10 / (29.8cosA + 7) = 7x 10 / (29.8cosA + 7) + 4
298sinA = 70 + 119.2cosA + 28
298 sqrt(1 - cos^2A) = 98 + 119.2cosA
sqyare both side
88804 - 88804cos^2A = 9604 + 14208.64cos^2 A + 23363.2cosA
103012.64cos^2A + 23363.2cosA - 79200 = 0
cosA = 0.770 and - 0.997
A = 39.65 degrees or 175.56 degrees
so at 39.65 degrees
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