Chapter 12.4, Problem 64E

### Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095

Chapter
Section

### Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095
Textbook Problem
3 views

# Projectile Motion A projectile is launched with an initial speed of 220 feet per second at a height of 4 feet and at an angle of 45 ∘ with the horizontal.(a) Determine the vector-valued function for the path of the projectile.(b) Use a graphing utility to graph the path and approximate the maximum height and range of the projectile.(c) Find v ( t ) , ‖ v ( t ) ‖ . and a(t).(d) Use a graphing utility to complete the table. t 0.5 1.0 1.5 2.0 2.5 3.0 Speed

(a)

To determine

To calculate: The vector-valued function for the path of the projectile.

Explanation

Given:

θ=45,v0=220ft/sec,h=4ft,g=32ft/s2

Formula used:

r(t)=(v0cosθ)ti+{h+(v0sinθ)t12gt2)}j

Calculation:

The path of the projectile of a vector-valued function is given by,

r(t)=(v0cosθ)

(b)

To determine

To graph: The path and approximate maximum height and range of projectile of given function.

(c)

To determine

To calculate: The values of v(t),v(t),a(t)

(d)

To determine

To calculate: The values to complete the table.

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