Exercise 51 Page 380

We want to find the speed of a falling apple when its kinetic energy is 32 joules using the formula for kinetic energy given in the exercise. First, let's take a look at a diagram that shows the change in kinetic energy. We are given a function that models the kinetic energy of a falling apple. K=v^2/2 In this formula, K is the kinetic energy in joules and v is the speed of the apple in meters per second. Let's substitute 32 for K in the given equation and solve for v. Since the value of v is squared, we will need to take the square root of both sides of the equation at some point. Let's do it!

K=v^2/2

Substitute

K= 32

32=v^2/2

MultEqn

LHS * 2=RHS* 2

64=v^2

SqrtEqn

sqrt(LHS)=sqrt(RHS)

sqrt(64)=sqrt(v^2)

SqrtPowToNumber

sqrt(a^2)=a

sqrt(64)=v

CalcRoot

Calculate root

8=v

RearrangeEqn

Rearrange equation

v=8

We found that the speed of a falling apple with a kinetic energy of 32 joules is 8 meters per second. Note that we do not need to consider the negative root because speed cannot be negative.