d)

The velocity of the particle when its height is 12 m is

> v5 := eval( V, t=5 );

> evalf( v5 );

>

Create a plot of the curve together with its tangent vector at t=5:

> r5 := eval( R, t=5 );

> evalf( r5 );

>

> plotR := spacecurve( R, PARAM, axes=boxed, color=BLUE ):

> plotV5 := plottools[arrow]( r5, r5+v5, .1, .2, .1, color=RED ):

> display( plotR, plotV5 );

>

Note: click on this graph to make the plot active. Use the mouse to grab and rotate a corner of the box to rotate the plot. Rotate the plot so that you see it from above (i.e., down the z axis). What are the traces in the x-z and y-z planes?

>