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A soccer player kicks a ball into the air at an angle of 34.0° above the horizontal. The initial velocity of the ball is +30.0 m/s. How long is the soccer ball in the air? = 34.0° Vi = +30.0 m/s Vy = Vi*sin t=? t = 2Vy/g Vy = 30.0Sin(34.0) = 16.8 m/s t = -2*16.8/-9.8 = 3.42 s What is the horizontal distance traveled by a soccer ball kicked into the air at an angle of 30.0° above the horizontal with initial velocity of +31.0 m/s? = 30.0° Vi = +31.0 m/s Dx = ? Vy = Vi*Sin Vx = Vi*Cos t = 2Vy/g Dx = t*Vx Vy = 31Sin(30) = 15.5 Vx = 31Cos(30) = 26.8 t = (-2*15.5)/-9.8 = 3.16 Dx = 3.16*15.5 = 84.6 m What is the maximum height of a soccer ball kicked into the air at an angle of 32.0° above the horizontal with the initial velocity of +25.0 m/s? = 32.0° Vi = 25.0 m/s Dy = ? Vy = 25Sin(32) = 13.2 m/s Dy = 13.22/(2*9.8) = 8.95 m Vy = Vi*Sin Dy = Vy2/2g A ball falls from rest from a height of 452 m. a. How long does it remain in the air? b. If the ball has a horizontal velocity of 1.00*102 m/s when it begins to fall, what horizontal displacement will it have? Dy = 452 m Vx = 1.00*102 t=? Dx = ? t2 = (2*452)/9.8 = √92.2 = 9.60 s Dx = 9.60*100 = 9.60*102 m t2 = 2Dy/g Dx = t*Vx An archer stands 40.0 m from the target. If the arrow is shot horizontally with a velocity of 87.0 m/s, how far above the bull’s-eye must she aim to compensate for gravity pulling her arrow downward? Dx = 40.0 m Vx = 87.0 m/s Dy = ? t = 40.0/87.0 = .459 s Dy = .5*9.8*.4592 = 1.04 m t = Dx/Vx Dy = .5gt2 A bridge is 142.9 m above a river. If a lead-weighted fishing line is thrown from the bridge with a horizontal velocity of 24.0 m/s, how far has it moved horizontally when it hits the water? Dy = 142.9 m Vx = 24.0 m/s Dx = ? t2 = (2*142.9)/9.8 = √29.2 = 5.40 s Dx = 5.4*24.0 = 1.30*102 m t2 = 2Dy/g Dx = t*Vx A beach ball, moving with a speed of +1.12 m/s, rolls off a pier and hits the water 0.65 m from the end of the pier. How high above the water is the pier? Vx = 1.12 m/s t = Dx/Vx Dx = 0.65 m Dy = .5gt2 Dy = ? t = 0.65/1.12 = .58 s Dy = .5*9.8*.582 = 1.7 m A shot put is released with a velocity of 12 m/s and stays in the air for 1.9 s. a. At what angle with the horizontal was it released? b. What horizontal distance did it travel? Vi = 12 m/s Vy = Vf-at t = 1.9 s θ = Sin-1(Vy/Vi) θ=? Vx = Vi*Cosθ Dx = ? Dx = Vx*t Vy = 0-9.8*0.95 = 9.3 m/s = Sin-1(9.3/12) = 51° Vx = 12Cos(51) = 7.6 m/s Dx = 7.6*1.9 = 14 m A football is kicked at 45° and travels 82 m before hitting the ground. a. What is the initial velocity? b. How long was it in the air? c. How high did it go? = 45° Dx = 82 m Vi = ? t=? Vi = √(g*Dx)/(2Sin*Cos) Vx = Vi*Cos t = Dx/Vx Vy = Vi*Sin Dy = Vy2/2g Dy = ? Vi = √(9.8*82)/[2Sin(45)Cos(45)] = 28 m/s Vx = 28Cos(45) = 20 m/s t = 82/20 = 4.1 s Vy = 28Sin(45) = 20 m/s Dy = 202/(2*9.8) = 20 m A golf ball is hit with a velocity of 46.0 m/s at 32.0° above the horizontal. Find a. The range of the ball b. The maximum height of the ball Vi = 46.0 m/s Range = Vi2Sin(2)/g = 32.0° Dy = Vy2/2g Range = 462Sin(2*32)/9.8 = 194 m 24.42/(2*9.8) = 30.3 m