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Pani-rosa [81]
3 years ago
7

An airplane with a speed of 92.3 m/s is climbing upward at an angle of 51.1 ° with respect to the horizontal. When the plane's a

ltitude is 532 m, the pilot releases a package.
(a) Calculate the distance along the ground, measured from a point directly beneath the point of release, to where the package hits the earth.
(b) Relative to the ground, determine the angle of the velocity vector of the package just before impact. (a) Number Units (b) Number Units
Physics
1 answer:
devlian [24]3 years ago
6 0

Answer:

a

D =  1162.7 \  m

b

\beta =- 65.55^o

Explanation:

From the question we are told that

  The speed of the airplane is  u  =  92.3 \ m/s

   The  angle is  \theta = 51.1^o

    The altitude of the plane is  d =  532 \  m

Generally the y-component of the airplanes velocity is  

       u_y  =  v *  sin (\theta )

=>     u_y  =   92.3 *  sin ( 51.1 )

=>     u_y  =  71.83  \ m/s

Generally the displacement  traveled by the package in the vertical direction is

       d =  (u_y)t +  \frac{1}{2}(-g)t^2

=>       -532  = 71.83 t +  \frac{1}{2}(-9.8)t^2

Here the negative sign for the distance show that the direction is along the negative y-axis

 =>   4.9t^2 - 71.83t - 532 = 0

Solving this using quadratic formula we obtain that

    t =  20.06 \  s

Generally the x-component of the velocity is  

     u_x  =  u  *  cos (\theta)

=>    u_x  =   92.3  *  cos (51.1)

=>   u_x  =   57.96 \ m/s

Generally the distance travel in the horizontal  direction is    

     D =  u_x  *  t

=>   D =  57.96  *   20.06

=>    D =  1162.7 \  m

Generally the angle of the velocity vector relative to the ground is mathematically represented as

       \beta  =  tan ^{-1}[\frac{v_y}{v_x } ]

Here v_y is the final  velocity of the package along the vertical  axis and this is mathematically represented as  

     v_y  =  u_y  -   gt

=>  v_y  =  71.83  -    9.8 *  20.06

=>  v_y  =  -130.05 \  m/s  

and  v_x is the final  velocity of the package which is equivalent to the initial velocity u_x

So

       \beta  =  tan ^{-1}[-130.05}{57.96 } ]

       \beta =- 65.55^o

The negative direction show that it is moving towards the south east direction

   

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