aballistossedintotheairat40feetpersecondfromaheightof5feet.howlongwillittaketheballtoreachtheground

Enter Projectile Motion Problem

  

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Set up the projectile motion equation:

h(t) = -16t² + vt + h where:
h = height, v = velocity, and t = time

Plug in our numbers to the projectile motion equation:

h(t) = -16t² + (40)t + 5

Since we want the time when the object hits the ground, we set h(t) = 0:

-16t² + 40t + 5 = 0

Since this is a quadratic equation, we solve it, ignoring any negative values, since height cannot be negative

The quadratic formula is denoted below:

=	-b ± √b2 - 4ac
	2a

Step 1 - calculate negative b:
-b = -(40)
-b = -40

Step 2 - calculate the discriminant Δ:
Δ = b² - 4ac:
Δ = 40² - 4 x -16 x 5
Δ = 1600 - -320
Δ = 1920 <--- Discriminant
Since Δ is greater than zero, we can expect two real and unequal roots.

Step 3 - take the square root of the discriminant Δ:
√Δ = √(1920)
√Δ = 8√30

Step 4 - find numerator 1 which is -b + the square root of the Discriminant:
Numerator 1 = -b + √Δ
Numerator 1 = -40 + 8√30

Step 5 - find numerator 2 which is -b - the square root of the Discriminant:
Numerator 2 = -b - √Δ
Numerator 2 = -40 - 8√30

Step 6 - calculate your denominator which is 2a:
Denominator = 2 * a
Denominator = 2 * -16
Denominator = -32

Step 7 - you have everything you need to solve. Find solutions:

Solution 1  =	Numerator 1
	Denominator

  Solution 1  =  (-40 + 8√30)/-32
Analyzing the 3 terms in our 1st answer, we see that -40, -32, and 8 are all divisible by 8
Dividing them all by 8, we get: -5, -4, and 1
  Solution 1  =  (-5 . 1√30)/-4

Solution 2  =	Numerator 2
	Denominator

  Solution 2  =  (-40 - 8√30)/-32
Analyzing the 3 terms in our 1st answer, we see that -40, -32, and 8 are all divisible by 8
Dividing them all by 8, we get: -5, -4, and 1
  Solution 2  =  (-5 - 1√30)/-4


As a solution set, our answers would be:

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Tags:

• height
• projectile motion
• quadratic equation
• velocity

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