Chapter 12.4, Problem 61E

### Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095

Chapter
Section

### Calculus

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

# Projectile Motion Find the tangential and normal components of acceleration for a projectile fired at an angle θ with the horizontal at an initial speed of v 0 . What are the components when the projectile is at its maximum height?

To determine

To Calculate: The normal and tangential components of acceleration for a projectile fired an angle θ with respect to the horizontal at an initial speed of vo. Also calculate the normal and tangential components when the projectile is at its maximum height.

Explanation

Given: Projectile is fired at an angle θ with respect to the horizontal component at an initial speed of vo

Formula Used:

if r(t)=a i+b j+c k||r(t)||=a2+b2+c2an=v×avaT=a.T

Calculation: From theorem position vector of a projectile, we understand that: r(t)=(v0tcosθ)i + (h +v0tsinθ16t2)jThen the velocity vector , v(t)=(v0cosθ)i+(v0sinθ32t)jThe acceleration vector, a(t) = -32jThe unit tangent vector T(t)= v(t)v(t)=v0cosθi+(v0sinθ32t)jv02cos2θ+(v0sinθ32t)2=v0cosθi+(v0sinθ32t)jv0264t v0sinθ+(32t)2differentiate,T(t),  with respect to t,      we getT|(t)=32jv0264t v0sinθ+(32t)2(64v0sinθ+32×32.2.t)[v0cosθi+(v0sinθ32t)]j2(v0264tv0sinθ+(32t)2)32=32(v0264t v0sinθ+(32t)2)j32(v0sinθ+32t)[v0cosθi+(v0sinθ32t)]j(v0264tv0s

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