LabWeek04 Projectile Motion-AG.docx

Figure 2 launch at an angel configuration data

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Figure 2: Launch at an Angel configuration Data Horizontal Launch Vertical Launch Launch at an Angle Trial Horizontal Displacement 1 228.5 cm 2 228.5 cm 3 230.0 cm 4 228.8 cm 5 230.6 cm 6 228.4 cm average 229.1 cm Vertical Displacement 110.9 cm Trial Maximum Height 1 127.3 cm 2 127.2 cm 3 127.5 cm 4 127.5 cm 5 127.2 cm 6 127.3 cm average 127.3 cm Vertical Displacement 111.3 cm Trial Horizontal Distance 1 109.0 cm 2 109.0 cm 3 109.1 cm 4 109.0 cm 5 109.3 cm 6 109.1 cm average 109.1 cm
Calculations Horizontal Launch Use horizontal motion: x = v ox t = v o t t = x v o (1) Substitute (1) into vertical motion: y = y o + v o t 1 2 gt 2 0 = y o 1 2 g ( x v o ) 2 Solve for v o : v o = g x 2 2 y 0 Using our data x = cm, y o = cm we find: v o = g x 2 2 y 0 = ( 9.81 ) x 2 2 y 0 v o = g x 2 2 y 0 Average Horizontal Distance: 2.291 m Vertical Displacement: 1.109 m Initial Speed: 4.818 m s
Vertical Launch Use vertical motion: v fy 2 = v oy 2 2 g∆ y Solve for v oy ( v oy = v o ): 0 = v oy 2 2 g ∆ y v oy 2 = 2 g∆ y v o = v oy = 2 g ∆ y v o = 2 g∆ y Average Vertical Displacement: 1.273 m Initial Speed: 4.998 m s
Launch at an Angle Use horizontal motion: x = x 0 + v 0 x t = v 0 x t x = v 0 cos ( θ ) .t t = x v 0 cos ( θ ) (3) Substitute (3) into vertical motion: y = y o + v oy t 1 2 gt 2 x v 0 cos ( θ ) ¿ ¿ 0 = y 0 + v 0 sin ( θ ) . x v 0 cos ( θ ) 1 2 g ¿ Solve for v 0 : v 0 = x cos ( θ ) . g 2 ( y 0 + x. tan ( θ ) ) v 0 = x cos ( θ ) . g 2 ( y 0 + x. tan ( θ ) )
Error Calculations Launch speed in m/s Horizontal: v 0 horizontal 4.818 m s Vertical: v 0 vertical 4.998 m s Angled: v 0 angle 2.302 m s Calculate the percentage error for the vertical launch from: | v 0 horizontal v 0 vertical | v 0 horizontal 100 = | 4.818 m s 4.998 m s | 4.818 m s 100 = 3.7 Calculate the percentage error for the angled launch from: | v 0 horizontal v 0 angle | v 0 horizontal 100 = | 4.818 m s 2.302 m s | 4.818 m s 100 = 52.22 Average Horizontal Distance: 1.091 m Vertical Displacement: 1.113 m Initial Speed: 2.302 m s
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