GREEN-SHEET-1995-02



Math 32 (01) Quiz Chapter-13 (50 Points) Last Name: _________________

(Saleem) Fall 2012 First Name: _________________

Show all work. Bold-faced letter are vectors. You are allowed to use a 3”x5” card of notes & a calculator.

#1(5 Points). Show all work and check whether the curve r(t) = lies on

the cone z2 = x2 + y2.

#2 (8 Points). Suppose you are traveling along the twisted cubic, r(t) = , where t is time and

the distances are in feet. Answer the following:

(a) At what time will your height above the ground be 64 feet?

(b) What is your speed (not velocity) at time t = 3 seconds? Leave square roots in the answer.

(c) What is your acceleration at t = 3. Write as a vector?

#3 (7 Points) The acceleration of a particle is, a(t) = . Find the velocity , v(t), if the

initial velocity vector is given by : v(0) = .

#4(20 Points) Consider the helix, r(t) = , where 0 ≤ t ≤ 6π, and “A” is a constant.

a) compute the unit tangent vector at t = π

b) compute the unit normal vector at t = π

c) compute the length from t=0 to t = 6π.

d) Find an expression for the curvature. Don’t plug any value for t, but simplify completely.

#5 (10 Points). A ball is thrown from ground level with an angle of elevation, 45o and a speed of 64 feet per second. The ball overshoots a target by 28 feet. At what angle must a second ball be fired with the same speed in order to hit the target? Take the value of g to be 32 ft/sec2. Give your answer in degrees.

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