to study damage to aircraft that collide with large birds youdesign a test gun t

Question

to study damage to aircraft that collide with large birds youdesign a test gun that will accelerate chicken-size objects so thattheir displacement along the gun barrel is given byx=(9.0*103m/s2)t2-(8.0*104m/s3)t3. the objects leave the end of the barrel att=0.025sec     a)how long must the gun barrel be ? b)what will be the speed of object as they leave the end ofthe barrel c)what net force must be exerted on 1.5kg objet at t=0 andt=0.025 to study damage to aircraft that collide with large birds youdesign a test gun that will accelerate chicken-size objects so thattheir displacement along the gun barrel is given byx=(9.0*103m/s2)t2-(8.0*104m/s3)t3. the objects leave the end of the barrel att=0.025sec     a)how long must the gun barrel be ? b)what will be the speed of object as they leave the end ofthe barrel c)what net force must be exerted on 1.5kg objet at t=0 andt=0.025

Explanation / Answer

The displacement along the gun barrel is x = (9.0*103m/s2)t2 -(8.0*104m/s3)t3-------------(1) The objects leave the end of the barrel at t = 0.025sec a)The length of the gun barrel is x = (9.0*103m/s2) * (0.025s)2- (8.0*104m/s3) * (0.025s)3 or x = 5.625m - 1.25m = 4.375 m b)The speed of the object as they leave the end of the barrelis v = (dx/dt) = (9.0*103m/s2) * (2t) -(8.0*104m/s3) * 3t2 When t = 0.025s,then v = (9.0*103m/s2) * (2 * 0.025s) -(8.0*104m/s3) * 3 *(0.025s)2 or v = 450 m/s - 150 m/s = 300 m/s c)The acceleration of the object is a = (dv/dt) = (d2x/dt2) =(9.0*103m/s2) * (2) -(8.0*104m/s3) * 6t When t = 0.025s,then a = (18.0*103m/s2) -(8.0*104m/s3) * 6 * (0.025s) or a = (18.0*103m/s2) - (1.2*104m/s2) or a = 1800 m/s2 - 1200 m/s2 = 600m/s2 The net force that must be exerted on the object at t = 0 andt = 0.025s is F = m * a Here,m = 1.5 kg or F = 1.5 * 600 = 900 N The net force that must be exerted on the object at t = 0 andt = 0.025s is F = m * a Here,m = 1.5 kg or F = 1.5 * 600 = 900 N

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