Question

Suppose an object is launched from ground level directly upward at 57.4 f/s Write a function to represent the object’s height over time.

Answer 1

To represent the object's height over time, you can use the equation h(t) = h0 + v0t - 16t^2, where h(t) is the height at time t, h0 is the initial height, v0 is the initial velocity, and t is the time elapsed.

Step-by-step explanation:

To write a function to represent the object's height over time, we need to first understand the basic principles of projectile motion. In this case, the object is launched directly upward at a velocity of 57.4 f/s. The height of the object over time can be determined using the equation:

h(t) = h0 + v0t - 16t^2

• h(t) represents the height of the object at time t
• h0 is the initial height of the object, which is 0 since it is launched from ground level
• v0 is the initial velocity of the object, which is 57.4 f/s
• t is the time elapsed

By plugging in the values into the equation, we can calculate the height of the object at any given time.

Answer 2

Answer: p(t) = (-16 ft/s^2)*t^2 + (57.4 ft/s)*t

Step-by-step explanation:

We can suppose that the only force acting on the object is the gravitational force, then the acceleration of the object will be equal to the gravitational acceleration.

Then we can write:

a(t) = -32 ft/s^2

Where the negative sign is because this acceleration is downwards.

Now, to get the vertical velocity of the object, we need to integrate over time to get:

v(t) = (-32 ft/s^2)*t + v0

where t represents time in seconds and v0 is the constant of integration, and in this case, is the initial vertical velocity.

In this case, the initial velocity is 57.4 ft/s upwards, then the velocity equation is:

v(t) = (-32 ft/s^2)*t + 57.4 ft/s

To get the position equation we need to integrate over time again, to get:

p(t) = (1/2)*(-32 ft/s^2)*t^2 + (57.4 ft/s)*t + p0

Where p0 is the initial height of the object, as it was launched from the ground, then the initial position is p0 = 0ft.

then the position equation (that is the function that represents the height of the object as a function over time) is:

p(t) = (1/2)*(-32 ft/s^2)*t^2 + (57.4 ft/s)*t

p(t) = (-16 ft/s^2)*t^2 + (57.4 ft/s)*t