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## Homework Statement

A bird flew along a helical path [tex]r(t)=<5cost,5sint,2t>[/tex], at time t=10 second, the bird died instantly. where did it hit the xy-plane ? g=32 ft/s/s.

## Homework Equations

[tex]r(t)=(v_0 \cos\theta t) i+(v_0 \sin\theta t - 0.5gt^2 + h_0) j[/tex]

## The Attempt at a Solution

taking derivative of r(t), I got the velocity function respect to t, [tex]v(t)=<-5sint,5cost,2>[/tex]

at t=10 s, we are located at (-4.2, -2.7, 20)

so that means the velocity in the x-direction at time =10 seconds is 2.72 ft/s

and the velocity in the y-direction at t=10 s = -4.2 ft/s

to hit the ground means that the distance in Z direction is 0, setting [tex]0=z(10)+v_z(10) t - 16t^2[/tex]

velocity in z direction is constant= 2

we can find the time the bird hit the ground, which = 1.18 second.

now, plug t and velocity in the x-direction into [tex]X_f=x(10)+v_x(10) t [/tex], we can find x-axis distance=-9.9 ft

[tex]Y_f=y(10)+v_y(10) t [/tex] similarly, we can find y - coordinate= -76.56 ft ( this value seems way off)

i am confused, does angle of projection matters in this case? if does, how do we find the angle of projection?

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