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

### Customer Question

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)?

Submitted: 5 years ago.
Category: Homework
Expert:  David replied 5 years ago.
David :

Hello, here is the solution.

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