First pic info, second pic questions Expert TA Login motion problem in which an

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First pic info, second pic questions Expert TA Login motion problem in which an object has an 40.0 m/ PROBLEM An Alaskan resoue plane drops emergency rations to stranded as shown in the figure. The plane is traveling horizontally at 40.0 m/s at a height of 1.00 x 102 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 of the velocity of the package just before it hits the ground? (c) Find the angle of the impact. From the point of view of an abserver on the ground, a package released from the rescue plane travels along the STRATEGY Here, we're just taking some path shown. filing in known quantites, and solving for the remaining unknown quantities, sketch the problem using a coordinate system asin the figure. In part (a), set the yoomponent of the displacement equations equal to -1.00 x 102 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 r- to find the range. n 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. SOLUTION (A) Find the range of the package. Use the equation to find the y O and 0, set y-- 90 m/s2x2 -1.00 x 102 m y 1.00 102 m, the final vertical position of the package relative the airplane. Solve for time. Use the equation to find the a- x (40.0 m/s)(4.52 181 m Substitute 0, vor 40.0 m/s, and the time, (B) Find the components of the package's velocity at impact. Find the x-component of the velocity at vx vocos 6 (40.0 m/s) cos o 40.0 m/s the time of impact. Find the y component of the velocity at vy vosin e-gr o (9,80 m/s?x4s2 s) the time of impact. H44.3 m/s (C) Find the angle of the impact. write the equation and substitute 1.11 40.0 m/s Apply the inverse tangent function to MORE REMARKS Notice how motion in the x-direction and motion in the direction are handled separately. QUESTION Neglecting air friction effects, what path does the package travel as observed by the plot? curved path that starts horizontal and then is increasingly bent downward curved path that is first curved upward and then downward downward curved path whose tangent line at each point has negative slope straight line saoped downward

Explanation / Answer

Given,

theta = 70 degrees

speed = 12m/s

: Vxo = Vo* cos70 = 12*cos 70 = 4.104 m/s

x = xo + vxo*t = 0 +  4.104[m/s] *t

V yo = vo*sin 70 = 11.276 m/s

y = y0+vyo*t - 0.5*gt^2 = 0 + 11.276 [m/s] *t - 4.9 [m/s^2] *t^2

===========================================

B)

t(flight) = 2*Vyo / g = 2*11.276 / 9.8 = 2.310 [s]

===========================================

c) angle is

T(flight) = 2*Vi*sin(theta)/g

equating to 0 and diff w.r.t to theta

2*Vi/g*cos(theta) = 0

theta=90 [degrees]

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