A cannonball is fired horizontally from the top of a cliff.The cannon is at heig
ID: 1682393 • Letter: A
Question
A cannonball is fired horizontally from the top of a cliff.The cannon is at height H = 80.0 m above groundlevel, and the ball is fired with initial horizontal speedv0. Assume acceleration due to gravity tobe g = 9.80 m/s.Assume that the cannon is fired attime t=0 and that the cannonball hits the ground at timetg. What is the y position of the cannonball atthe time tg/2? This answer is 60 m. Given that the projectile lands at adistance D = 150 m from the cliff, as shown inthe figure, find the initial speed of the projectile,v0. A cannonball is fired horizontally from the top of a cliff.The cannon is at height H = 80.0 m above groundlevel, and the ball is fired with initial horizontal speedv0. Assume acceleration due to gravity tobe g = 9.80 m/s.
Assume that the cannon is fired attime t=0 and that the cannonball hits the ground at timetg. What is the y position of the cannonball atthe time tg/2? This answer is 60 m. Given that the projectile lands at adistance D = 150 m from the cliff, as shown inthe figure, find the initial speed of the projectile,v0. Assume that the cannon is fired attime t=0 and that the cannonball hits the ground at timetg. What is the y position of the cannonball atthe time tg/2? This answer is 60 m. Given that the projectile lands at adistance D = 150 m from the cliff, as shown inthe figure, find the initial speed of the projectile,v0.
Explanation / Answer
acceleration ay =-g velocity vy = -gt + vy0 position y = -gt2/2 + vy0t + y0 acceleration ax = 0 velocity vx = vx0 position x = vx0*t + x0 Now vy0 = 0, y0 = H, giving us vy = -gt y = -gt2/2 + H If the cannonball hits the ground at tg, theny(tg) = 0, y(tg) = -gtg2/2 + H = 0 ----> tg = (2H/g) y(tg/2) = -g*H/(2*2g) + H = -H/4 + H =3H/4 = 240 / 4 = 60 mThe initial speed of the projectile is x(tg) = vx0*tg = vx0*(2H/g) =150 ==> vx0 = 150/(2H/g) = 150/(2*80/9.80) = 37.123 m/s
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