Identify the function that models (ignoring air resistance) a ball being thrown in the air with an initial velocity of 70 ft/s, from a height of 5 feet.
To identify the function that models the motion of a ball being thrown in the air, we can use the kinematic equation for vertical motion. Ignoring air resistance, the equation is given as:
h(t) = -16t^2 + vt + h₀
Where:
- h(t) represents the height of the ball at time t
- v represents the initial velocity of the ball
- t represents the time in seconds
- h₀ represents the initial height from which the ball is thrown
In this case, the initial velocity (v) is given as 70 ft/s, and the initial height (h₀) is given as 5 feet.
Substituting these values into the equation, we get:
h(t) = -16t^2 + 70t + 5
Therefore, the function that models the ball being thrown in the air (ignoring air resistance) is h(t) = -16t^2 + 70t + 5.