Respuesta :
We have been given that a football is kicked into the air with an initial upward velocity of 82 feet per second. The height (H) of ball in feet is recorded at various second in the table. We are asked to write an equation that represents the given scenario.
We know that equation of height of an upward moving object is [tex]h(t)=-\frac{1}{2}gt^2+V_0t+h_0[/tex], where,
g = Acceleration due to gravity,
[tex]V_0[/tex] = Initial velocity,
[tex]h_0[/tex] = Initial height.
[tex]V_0=82[/tex] and [tex]h_0=0[/tex]. We know that acceleration due to gravity is a constant and its value is 32 feet square per sec.
Upon substituting these values, we will get:
[tex]h(t)=-\frac{1}{2}(32)t^2+82t+0[/tex]
[tex]h(t)=-16t^2+82t[/tex]
Therefore, the equation [tex]h(t)=-16t^2+82[/tex] represents the height of the football after t seconds.
To find the height of the football after 5 seconds, we will substitute [tex]t=5[/tex] in our equation as:
[tex]h(5)=-16(5)^2+82(5)[/tex]
[tex]h(5)=-16(25)+410[/tex]
[tex]h(5)=-400+410[/tex]
[tex]h(5)=10[/tex]
Therefore, the height of the football after 5 seconds would be 10 feet.
Equation for the curve of best fit → [tex]h(t)=-16t^2+84t[/tex]
Height of the football after 5 seconds = 10 feet
Equation of motion in upwards direction:
- If a football is kicked upwards with an initial velocity [tex]v_0[/tex], height attained by the football at time 't' will be given by,
[tex]h(t)=v_0t-\frac{1}{2}gt^2+h_0[/tex]
Here, g = gravitation constant = 16 feet per second square
[tex]h_0=[/tex] Initial height from where the ball is kicked
From the table attached,
- At t = 0, h(0) = 0,
[tex]v_0=82[/tex] meter per second
Substitute these values in the equation,
[tex]0=v_0(0)-\frac{1}{2}g(0)+h_0[/tex]
[tex]h_0=0[/tex]
Therefore, equation will be,
[tex]h(t)=82t-\frac{1}{2}(16)t^2[/tex]
[tex]h(t)=-16t^2+82t[/tex]
2. At t = 5 seconds,
[tex]h(5)=-16(5)^2+82(5)[/tex]
[tex]=10[/tex] feet
Therefore, equation for the curve of best fit → [tex]h(t)=-16t^2+82t[/tex]
Height of the football after 5 seconds = 10 feet
Learn more about the motion in upward direction here,
https://brainly.com/question/2288868?referrer=searchResults
