Question

an object is thrown off a platform that is 15 ft high with an initial velocity of 8.5 ft/is what function models the height h of the object after t seconds

Answer 1

The height of the object after t seconds can be modeled by the equation h(t) = -16t^2 + 8.5t + 15, which factors in the initial height, initial velocity, and the acceleration due to gravity.

Step-by-step explanation:

The function that models the height h of an object after t seconds when it is thrown off a platform with a given initial height and initial velocity can be described using the kinematic equation for projectile motion under gravity. Since the object is thrown from a height of 15 ft with an initial vertical velocity of 8.5 ft/s, the equation to model the height of the object at any time t would be:

h(t) = -16t2 + 8.5t + 15

Here, -16 represents half of the acceleration due to gravity in ft/s2 (since gravity = 32 ft/s2), 8.5t represents the initial velocity in feet per second (ft/s), and 15 is the initial height in feet.

Answer 2

Therefore the function that models the height of the object after t seconds is given by "H(t) = 15 + 8.5*t + 16.09*t²".

Step-by-step explanation:

Since the object has a initial velocity and it's being accelerated by gravity, than it's height is defined by:

H(t) = H(0) + V(0)*t + 0.5*g*t²

Applying the data from the problem, we have:

H(t) = 15 + 8.5*t + 0.5*32.17405*t²

H(t) = 15 + 8.5*t + 16.09*t²

Therefore the function that models the height of the object after t seconds is given by "H(t) = 15 + 8.5*t + 16.09*t²".