1 .		A particle moves along the curve r(t) = ti + 2t2j + t3k. Find its velocity and acceleration at the instant when the particle is at the point (-1, 2, -1).
2 .		The path followed by a particle experiencing a constant downward acceleration, -gj, caused by gravity can be described in the xy plane by (see diagram). Denote |v0| = v0 and express r(t) in terms of v0, θ, and h.
3 .		A baseball is hit one metre above ground level at 30 m/s and at an angle of 45° with respect to the ground. Find the approximate maximum height reached by the baseball.
4 .		Given that , solve the initial-value problem
5 .		Which set of parametric equations does not represent the first quadrant portion?
6 .		The plane y = 1 intersects the cone z² = x² + y² in a hyperbola. Find a parameterization of the hyperbola.
7 .		Find the length of the curve
8 .		Find the arc length of the given curve on the interval [0, π/2].
9 .		Parameterize the circle x² + y² = a² in terms of the arc length measured from the point (a, 0) in the counter clockwise direction.
10 .		Find the unit tangent and the principal unit normal vectors to the curve
11 .		Find the curvature of the curve
12 .		Find the Frenet frame, , for the curve at the point (2,0,0).
13 .		Find the tangential and normal components of acceleration of a particle whose position vector is given by
14 .		The Earth has an elliptical orbit with an eccentricity of e ≈ 0.0167 and a semi-major axis a ≈ 92.957 × 106 miles. Find the polar equation of the elliptical orbit of the Earth.
15 .		The Earth has an elliptical orbit with an eccentricity of e ≈ 0.0167 and a semi-major axis a ≈ 92.957 × 106 miles. Find the perihelion (nearest Earth is to the Sun) and the aphelion (furthest Earth is from the Sun) of the Earth’s orbit.
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