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An Airplane Is Flying With A Velocity Of 240 M/S At An Angle

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An airplane is flying with a velocity of 240 m/s at an angle of 30 degrees with the horizontal (in a downward dive). When the altitude of the plane is 2.4 KM a flare is released from the plane. The flare hits the target on the ground. What is the angle theta (angle between line of sight and ground)?

We have the initial velocity of the flare is 240 m/s at 30 deg below horizontal First we calculate the time it takes to reach the ground: h=vo*t*sin(30)+0.5gt^2 2400 = 240*t*0.5+4.9t^2 2400 = 120*t+4.9t^2 positive solution of this quadratic equation is t=13.05 sec the negative solution is not physical. now calculate the vertical speed of the flare just before it hits the ground Vy = Vosin(30)+gt = 120+9.8*13.05 = 247.89 and horizontal velocity is Vx= Vocos(30)=207.85 so the angle we are looking for is: theta = atan(Vy/Vx) = atan(247.89/207.85)=50 degrees

Answer: 50 degrees below horizontal

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