separately. QUESTION Neglecting air friction effects, what path does the package travel as observed by the pilot a downward curved path whose tangent line at each point has negative slope O a curved path that is first curved upward and then downward O a straight line sloped downward O a vertical line downward O a curved path that starts horizontal and then is increasingly bent downward
separately. QUESTION Neglecting air friction effects, what path does the package travel as observed by the pilot a downward curved path whose tangent line at each point has negative slope O a curved path that is first curved upward and then downward O a straight line sloped downward O a vertical line downward O a curved path that starts horizontal and then is increasingly bent downward
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Which option is correct?
Transcribed Image Text:GOAL Solve a two-dimensional projectile motion problem in which an object has an initial horizontal
velocity.
40.0 m/s
100 m
From the point of view of an observer on the
ground, a package released from the rescue
plane travels along the path shown.
PROBLEM An Alaskan rescue plane drops a package of emergency rations to stranded hikers, as shown
in the figure. The plane is traveling horizontally at 40.0 m/s at a height of 1.00 x 10 m above the
ground. (a) Where does the package strike the ground relative to the point at which it was released?
(b) What are the horizontal and vertical components of the velocity of the package just before it hits the
ground? (c) Find the angle of the impact.
STRATEGY Here, we're just taking some equations, filling in known quantities, and solving for the
remaining unknown quantities. Sketch the problem using a coordinate system as in the figure. In part (a),
set the y-component of the displacement equations equal to -1.00 x 10 m-the ground level where the
package lands-and solve for the time it takes the package to reach the ground. Substitute this time into
the displacement equation for the x-component to find the range. In part (b), substitute the time found in
part (a) into the velocity components. Notice that the initial velocity has only an x-component, which
simplifies the math. Solving part (c) requires the inverse tangent function.
Transcribed Image Text:(A) Find the range of the package.
Use the equation to find the y-
displacement.
Ay =y-Yo Voy-gt
Substitute yo = 0 and vo,= 0, set
Voy
y =- (4.90 m/s?)t2 - -1.00 x 102 m
KEMAKKS Notice now motion in the x-direction and motion in the y-direction are handled separately.
y = -1.00 = 102 m, the final vertical
position of the package relative the
airplane. Solve for time.
t- 4.52 s
QUESTION Neglecting air friction effects, what path does the package travel as observed by the pilot?
O a downward curved path whose tangent line at each point has negative slope
Use the equation to find the x-
Ax = x - Xo = Vont
displacement.
O a curved path that is first curved upward and then downward
O a straight line sloped downward
Substitute xo = 0, vo, = 40.0 m/s,
x = (40.0 m/s)(4.52 s) = 181 m
O a vertical line downward
and the time.
O a curved path that starts horizontal and then is increasingly bent downward
(B) Find the components of the package's velocity at impact.
Find the x-component of the velocity at
v = Vcos e = (40.0 m/s) cos 0° = 40.0 m/s
the time of impact.
Find the y-component of the velocity at
the time of impact.
Vy = Vosin e - gt = 0 - (9.80 m/s²)(4.52 s)
= -44.3 m/s
%3D
(C) Find the angle of the impact.
Write the equation and substitute
-44.3 m/s
tan 8 =
= -1.11
values.
40.0 m/s
Apply the inverse tangent function to
e= tan-(-1.11) = -48.0°
%3!
both sides.
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