Velocity and Acceleration

A baseball player at second base throws a ball 90 feet to the player at first base. The ball is thrown
 at 50 miles per hour at an angle of 15 above the horizontal. At what height does the player at first base catch the ball if the ball is thrown from a height of 5 feet?
A projectile is fired from ground level at an angle of 12
 with the horizontal. Find the minimum initial velocity if the projectile is to have a range of 150 feet.

Tangent Vectors and Normal
Vectors

1) Find the unit tangent vector and find a set of parametric equations for the line tangent to the space curve at the point P.
 r ( t )
 t , t , 4
 t
2
P ( 1 , 1 , 3 )
2) Find the principal unit normal vector to the curve above at the specified point.

For plane curves, you can find the principal unit normal vector by finding T (t)= x ( t ) i
 y ( t ) j and then observe that N (t) will either be
N
2
( t )
  y ( t ) i
 x ( t ) j OR N
2
( t )
  y ( t ) i
 x ( t ) j
It will be the one that points toward the concave side of the curve.

1) Find T (t), N a for the given curve r(t) a
N r t
2 i

2 r e t cos ti
 e t sin tj
 e t