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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)?
Hello, here is the solution.
We have the initial velocity of the flare is 240 m/s at 30 deg below horizontalFirst we calculate the time it takes to reach the ground:h=vo*t*sin(30)+0.5gt^22400 = 240*t*0.5+4.9t^22400 = 120*t+4.9t^2positive solution of this quadratic equation is t=13.05 secthe negative solution is not physical.now calculate the vertical speed of the flare just before it hits the groundVy = Vosin(30)+gt = 120+9.8*13.05 = 247.89and horizontal velocity isVx= Vocos(30)=207.85so the angle we are looking for is:theta = atan(Vy/Vx) = atan(247.89/207.85)=50 degrees
Answer: 50 degrees below horizontal
Hope this helps.