For given conditions the value of the velocity v is 90 ft/sec.
And for original equation, when t = 0, the value of the velocity v is undefined.
"It is a mathematical statement which consists of equal symbol between two algebraic expressions."
"It is the rate of change of displacement."
For given question,
The equation below describes the height, h, of the t-shirt, t seconds after it is shot from the cannon c feet above the ground, at an initial velocity of v.
[tex]h = -16t^2 + vt + c[/tex] .............(1)
We need to solve the equation for initial velocity, v.
The cannon launched a t-shirt from an initial height of 5 feet.
⇒ c = 5 ft.
After 3 seconds the shirt has reached a height of 131 feet.
This means, for t = 3 seconds, h = 131 ft
So, an equation would be,
⇒ 131 = -16(3)² + v(3) + 5
⇒ 131 = -16 × 9 + 3v + 5
⇒ 3v = 270
⇒ v = 90 ft/sec
This means, the initial velocity v is 90 ft/sec
From equation (1),
⇒ h = -16t² + vt + c
⇒ h - c = -16t² + vt
⇒ h - c + 16t² = vt
⇒ [tex]v=\frac{ h - c + 16t^2}{t}[/tex]
When t = 0,
the value of the velocity, v is not defined ([tex]\infty[/tex]).
This means, when t = 0, the value of the velocity v is undefined.
Therefore, for given conditions the value of the initial velocity v is : 90 ft/sec.
And for original equation, when t = 0, the value of the velocity v is undefined.
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