Exam 12: Vector-Valued Functions

The quarterback of a football team releases a pass at a height of 6 feet above the playing field, and the football is caught by a receiver 34 yards directly downfield at a height of 3 feet. The pass is released at an angle of $45 ^ { \circ } \text { with the horizontal. Find the time in seconds the receiver has }$ to reach the proper position after the quarterback releases the football. Round your answer to one Decimal place.

(Multiple Choice)

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Question 81

Find the principle unit normal vector to the curve given below at the specified point. $\mathbf { r } ( t ) = t \mathbf { i } + 4 t ^ { 2 } \mathbf { j } , \quad t = 3$

(Multiple Choice)

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Question 82

Sketch the curve represented by the vector-valued function $\mathbf { r } ( t ) = \cos t \mathbf { i } + \sin t \mathbf { j } + t \mathbf { k }$ and give the orientation of the curve.

(Multiple Choice)

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Question 83

Find the principle unit normal vector to the curve given below at the specified point. $\mathbf { r } ( t ) = t \mathbf { i } + 4 t ^ { 2 } \mathbf { j } , \quad t = 3$

Sketch the curve represented by the vector-valued function $\mathbf { r } ( t ) = \cos t \mathbf { i } + \sin t \mathbf { j } + t \mathbf { k }$ and give the orientation of the curve.

Graphs and Models

A Preview of Calculus

The Derivative and the Tangent Line Problem

Extrema on an Interval

Antiderivatives and Indefinite Integration

Slope Fields and Eulers Method

Area of a Region Between Two Curves

Basic Integration Rules

Sequences

Conics and Calculus

Vectors in the Plane

Introduction to Functions of Several Variables

Iterated Integrals and Area in the Plane

Vector Fields

Exact First-Order Equations

Filters

Exam 12: Vector-Valued Functions

Find the principle unit normal vector to the curve given below at the specified point. r(t)=ti+4t2j,t=3\mathbf { r } ( t ) = t \mathbf { i } + 4 t ^ { 2 } \mathbf { j } , \quad t = 3r(t)=ti+4t2j,t=3

Sketch the curve represented by the vector-valued function r(t)=cos⁡ti+sin⁡tj+tk\mathbf { r } ( t ) = \cos t \mathbf { i } + \sin t \mathbf { j } + t \mathbf { k }r(t)=costi+sintj+tk and give the orientation of the curve.

Graphs and Models

A Preview of Calculus

The Derivative and the Tangent Line Problem

Extrema on an Interval

Antiderivatives and Indefinite Integration

Slope Fields and Eulers Method

Area of a Region Between Two Curves

Basic Integration Rules

Sequences

Conics and Calculus

Vectors in the Plane

Introduction to Functions of Several Variables

Iterated Integrals and Area in the Plane

Vector Fields

Exact First-Order Equations

Filters

Find the principle unit normal vector to the curve given below at the specified point. $\mathbf { r } ( t ) = t \mathbf { i } + 4 t ^ { 2 } \mathbf { j } , \quad t = 3$

Sketch the curve represented by the vector-valued function $\mathbf { r } ( t ) = \cos t \mathbf { i } + \sin t \mathbf { j } + t \mathbf { k }$ and give the orientation of the curve.