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 Vector Functions and Curves Multiple Choice Quizzes

 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. Answer choices in this exercise are randomized and will appear in a different order each time the page is loaded.