The given question have mistake. The correct question is written below.
Question:
A dog jumps straight up in the air to catch a ball and lands on the ground 6.37 s later. Let h(t) represent the dog’s height, in meters, t seconds after he leaves the ground. Which equation models the dog’s height for a given time t?
Answer:
Option B:
[tex]h(t)=-4.9 t^{2}+6.37t[/tex]
Solution:
General formula for the height of the projectile over time:
(1) [tex]h(t)=-16 t^{2}+v t+s[/tex]
Where h = height in feet, t = time, v = initial velocity and s = initial height (feet)
(2) [tex]h(t)=-4.9 t^{2}+v t+s[/tex]
Where h = height in meters, t = time, v = initial velocity and s = initial height(meter)
Given initial velocity = 6.37 s and initial height is 0.
The height of the dog is in meters.
So, use second formula and substitute v = 6.37 and s = 0.
[tex]h(t)=-4.9 t^{2}+v t+s[/tex]
[tex]h(t)=-4.9 t^{2}+6.37t+0[/tex]
[tex]h(t)=-4.9 t^{2}+6.37t[/tex]
Hence option B is the correct answer.
