BC Calc III
Sample Vector Quiz
Name:
Calculator allowed.
You must show enough work so that I can recreate your results.
#1.
Let v  5i  3 j . Find
a. the magnitude of v
b. a unit vector in the direction of v
#2.
32
 j , v (0)  15 i  20 j , r (0)  15 i , where
t 1
a (t ), v (t ), and r (t ) represent the acceleration, velocity, and position vectors
respectively.
Suppose that a (t ) 
a. Find v (t ) and r (t ) .
b. Find the speed at time t = 0.
c. Set up an integral that gives the total distance traveled for 0  t  1.
BC CALC III
#3. A diver leaps from the edge of a diving platform into a pool below. The figure below
shows the initial position of the diver and her position at a later time. At time t seconds after
she leaps, the horizontal distance from the front edge of the platform to the diver’s
shoulders is given by x(t ) , and the vertical distance from the water to her shoulders is given
by y (t ) where x(t ) and y (t ) are measured in meters. Suppose that the diver’s shoulders are
11.4 meters above the water when she makes her leap and that
dx
dy
 0.8 and
 3.6  9.8t for 0  t  A , where A is the time when the diver’s shoulders
dt
dt
enter the water. Use your calculator on this problem, but show set-up clearly.
a. Find the maximum vertical distance
from the water surface to the diver’s
shoulders.
x(t)
y(t)
b. Find A, the time when the diver’s shoulders enter the water.
c. Find the total distance travelled by the diver’s shoulders for 0  t  A .
d. Find the angle  , 0   
t  A.
BC CALC III

2
, between the path of the diver and the water at the time