What is the justification for step 1
1 answer:
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Answer:
Kerry's ball stays longer in the air than Marias ball by an extra 0.582 seconds
Step-by-step explanation:
The equation that models the height, h, in feet of object thrown modeled as a time function is given as follows;
h(t) = -16t² + v₀·t + h₀
Where;
v₀ = The velocity upwards (vertical velocity)
h₀ = The initial height of the object in feet
The given parameters are;
The initial height from which Maria throws a ball = 6 feet
The initial vertical velocity with which Maria throws the ball = 40 feet per second
The initial height from which Kerry throws a ball = 5 feet
The initial vertical velocity with which Kerry throws the ball = 50 feet per second
For Maria, from the equation for the height of the object, we have;
h(t) = -16t² + v₀·t + h₀
Where for Maria, we have;
h₀ = 6 feet
v₀ = 40 ft/s
Substituting gives;
h(t) = -16 × t² + 40 × t + 6 = -16·t² + 40·t + 6
h(t) = -16·t² + 40·t + 6
The time it takes for the ball to go up and come back down again is given by the value of t, when h = 0 (ground level) as follows;
0 = -16·t² + 40·t + 6
16·t² - 40·t - 6 = 0
From the quadratic formula, we have
t ≈ 2.64 s or -0.14 s
Therefore, the time the ball spends in the air ≈ 2.64 s
For Kerry, we have;
h₀ = 5 feet
v₀ = 50 ft/s
Substituting gives;
h(t) = -16 × t² + 50 × t + 5 = -16·t² + 50·t + 5
h(t) = -16·t² + 50·t + 5
Which gives;
16·t² - 50·t - 5 = 0
From the quadratic formula, we have
t ≈ 3.222 s or -0.097 s
he time the ball spends in the air ≈ 3.222 s
Therefore, Kerry's ball that spends approximately 3.222 seconds stays longer in the air than Maria's ball that spends approximately 2.64 seconds in the air.
The difference in the two time duration is 3.222 - 2.64 = 0.582
Kerry's ball stays longer in the air than Marias ball by an extra 0.582 seconds.