Question Solved1 Answer Problem begins here: A wooden ball of weight 196 newtons is dropped vertically from a height of 100 meters above the ground. Throughout the fall, drag is present by a factor 4v due to air resistance, where v is the velocity of the ball at time t (in seconds). After how many seconds will the ball impact the ground? Assume that the net force acting on the ball is modeled by m(dv/dt) = mg - kv, where m is the mass of the ball. Also, assume that there is no initial velocity and that the acceleration due to gravity g is 9.8 meters per second squared. Do not round off intermediate steps. Round off the final answer to two decimal places. Choose the correct answer from among the given choices. A) 1.23 seconds 2.89 seconds 3.25 seconds 4.01 seconds E) 4.20 seconds F 5.00 seconds G 5.31 seconds (H) 6.20 seconds Ousstian 2
WK6G5K The Asker · Calculus
Transcribed Image Text: Problem begins here: A wooden ball of weight 196 newtons is dropped vertically from a height of 100 meters above the ground. Throughout the fall, drag is present by a factor 4v due to air resistance, where v is the velocity of the ball at time t (in seconds). After how many seconds will the ball impact the ground? Assume that the net force acting on the ball is modeled by m(dv/dt) = mg - kv, where m is the mass of the ball. Also, assume that there is no initial velocity and that the acceleration due to gravity g is 9.8 meters per second squared. Do not round off intermediate steps. Round off the final answer to two decimal places. Choose the correct answer from among the given choices. A) 1.23 seconds 2.89 seconds 3.25 seconds 4.01 seconds E) 4.20 seconds F 5.00 seconds G 5.31 seconds (H) 6.20 seconds Ousstian 2
More Transcribed Image Text: Problem begins here: A wooden ball of weight 196 newtons is dropped vertically from a height of 100 meters above the ground. Throughout the fall, drag is present by a factor 4v due to air resistance, where v is the velocity of the ball at time t (in seconds). After how many seconds will the ball impact the ground? Assume that the net force acting on the ball is modeled by m(dv/dt) = mg - kv, where m is the mass of the ball. Also, assume that there is no initial velocity and that the acceleration due to gravity g is 9.8 meters per second squared. Do not round off intermediate steps. Round off the final answer to two decimal places. Choose the correct answer from among the given choices. A) 1.23 seconds 2.89 seconds 3.25 seconds 4.01 seconds E) 4.20 seconds F 5.00 seconds G 5.31 seconds (H) 6.20 seconds Ousstian 2
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Step 1Answer is mentioned belowStep 2The equation modelling the physical problem is,m(dv)/(dt)=mg-kv-(1)Here, k=4{:[mg=196N],[m=(196)/(9.8)=20kg]:}The ball is droped from height of 100m.:. equation (1) becomes{:[(dv)/(dt)=(mg-kv)/(m)=(196-4v.)/(20)],[=>(dv)/(196-4v)=(dt)/(20)],[(dv)/(4(49-v))=(dt)/(20)]:}Integrating this equation, we get{:[(-1)/(4)ln(49-v)=(1)/(20)t+c],[ln(49-v)=(-4)/(20)t-c_(1)],[49-v=e^(-(4)/(20)t-c_(1))],[49-v=c_(3)e^(-t//5)],[v=49-c_(3)e^(-t//5)]:}given initial velocity V=0 at t=0Step 3{:[=>0=49-c_(3)],[=>c_(3)=49],[:.v(t)=49(1-e^(-t//5))m//s]:}is the intant ... See the full answer