Map Sapling Learning macmillan learning You would like to shoot an orange in a t

Question

Map Sapling Learning macmillan learning You would like to shoot an orange in a tree with your bow and arrow. The orange is hanging 5.00 m above the ground. On your first try, you fire the arrow at 32.0 m/s at an angle of 30.0° above the horizontal from a height of 1.20 m while standing 50.0 m away. Treating the arrow as a point projectile and neglecting air resistance, what is the height of the arrow once it has traveled the 50.0 m horizontally to the tree? 30.0° 5.00 m 1.20 m 50.0 m Number Im It you fire at the same speed and angle on your second try, how far away could you stand such that the arrow will hit the orange? Assume that the orange remains fixed in place during the arrow's flight. Select all that apply 81.8 m 8.6 m 7.1 m 51.5 m 83.3 m Previous Give Up & View Solution V Check Answer Next Exit

Explanation / Answer

a) In the horizontal component of the arrow's motion, the horizontal velocity remains constant; therefore,

dx = (v_0)*(t), dx = 50.0 m i and v_0 = 32.0cos(30) m/s i

t = dx/(v_0) = (50.0) / (32.0*cos(30)) = 1.804 s

In this amount of time, the arrow should have been vertically displaced such that:

yf = y0 + v0(t) + 0.5a(t)^2

Given that the initial height y0 is 1.20 m j, the initial velocity v0 is 32.0sin(30) m/s j, the flight time t is 1.804 s,

Also, the acceleration a is g or -9.8 m/s^2 j,

Therefore, from above equation ,we get
yf = 1.20 + 32.0sin(30)(1.804) + 0.5(-9.8)(1.804)^2

yf = 14.117 m j


b) By standing at another horizontal distance away from the orange, the flight time and the horizontal displacement will change:

yf = y0 + v0t + 0.5at^2;

If the final height yf is to be 5.00 m j,

5.00 = 1.20 + 32.0sin(30)(t) + 0.5(-9.8)(t)^2

t = 0.7755 s or t = 3.46 s

Plug these values into the equation for horizontal displacement.
If the flight time is 0.7755 s, the arrow could be horizontally displaced by

d=v*t = v0*0.7755= =32.0cos(30)*0.7755 = 21.491 m i;

On the other hand, if the flight time is 3.46 s, the horizontal displacement will then be

d=v0*t= 95.886 m i

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