The coordinates of a bird flying in the xy-plane are given by x(1-al and y(1) 3.

Question

The coordinates of a bird flying in the xy-plane are given by x(1-al and y(1) 3.0 m-B12, where -2.4 m/s and B 1.2 m/st. (a) Sketch the path of the bird between0 and 1 = 2.0 s. (b) Calculate the velocity and acceleration vectors of the bird as functions of time. (c) Calculate the magnitude and direction of the bird's velocity and accelertion at 1=2.0 s. (d) Sketch the velocity and acceleration vectors at 2.0 s. At this instant., is the bird speeding up, is it slowing down, or is its peed instantaneously not changing? Is the bird urning? If so, in what direction? Yum)

Explanation / Answer

X(t)=2.4t, y(t)=3.0-1.2t².

b) x’(t)=2.4, y’(t)=-2.4t. v={x’(t), y’(t)}=(2.4, -2.4t).

x’’(t)=0, y’’(t)=-2.4. a={x’’(t), y’’(t)}=(0, -2.4).

c) |v|=|(2.4, -2.4t)|={2.4²+(-2.4t)²}=

2.4(1+t²)v(2.0)=2.45=5.367m/s.

From b) tan(t)=-t=-2.0 at t=2.0

=360-63.43=297°.

|a|=(0²+(-2.4)²)= 2.4m/s².

By b) a is 2.4m/s² in the –y direction

and so is 270° counterclockwise.

d) By c) |a|=2.4m/s²>0, so bird is

speeding up all the time.

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