Question

An aeroplane is flying with a velocity of 90 m/s at an angle of 23 degree above the horizontal.when the plane is 114m directly above a dog that is standing on level ground .a suitcase is drops out of luggage compartment.how far from the dog will the suticase land

Answer 1

We consider that the trajectory is parabola.

Both the vertical parabola and horizontal parabola are observed.

Answer 2

Therefore 795.36 m from the dog , the suitcase will be landed.

An aeroplane is flying with a velocity of 90 m/s at an angle of 23° above the horizontal. When the plane is 114m directly above a dog that is standing on level ground . A suitcase is drops out of luggage compartment.

How far from the dog will the suitcase land ?

at the height of 114 m, A suitcase is dropped out from the plane.

horizontal components of velocity of plane,

$u_x=ucos23^{\circ}$

= 90cos23° ≈ 82.85 m/s

vertical components of velocity of plane,

$u_y=usin23^{\circ}$

= 90sin23° ≈ 35.17 m

we know,

$y=u_yt+\frac{1}{2}a_yt^2$

⇒-114 m = +35.17 × t + 1/2 × -9.8 × t²

⇒4.9t² -35.17t - 114 = 0

after solving it we get, t ≈ 9.6 sec

now using,

$x=u_xt+\frac{1}{2}a_xt^2$

⇒x = 82.85 m/s × 9.6 sec + 0

= 795.36 m

Therefore 795.36 m from the dog , the suitcase will be landed.