Two identical rubber balls are dropped from different heights. Ball 1 is dropped from a height of 156 feet, and ball 2 is dropped from a height of 202 feet. Write a function for the height of each ball.
h1(t)=159+t
h2(t)=202+t
look at your functions. They indicate that the ball rises as time goes on, and never comes back down.
h1(t) = 156 - 16t^2
To find the height of each ball as a function of time, we can use a simple kinematic equation. The equation for the height of an object in free fall is:
h(t) = h0 + v0 * t + (1/2) * g * t^2
Where:
- h(t) is the height of the object at time t.
- h0 is the initial height of the object (the height from which it was dropped).
- v0 is the initial velocity of the object (which is 0 for objects dropped from rest).
- t is the time elapsed since the object was dropped.
- g is the acceleration due to gravity (which is approximately 32.2 ft/s^2 or 9.8 m/s^2).
In this case, both balls are dropped from rest (so v0 = 0), and we are given the initial heights (h0) as 156 ft and 202 ft for ball 1 and ball 2 respectively.
Using the given information, we can write the functions for the height of each ball as a function of time:
h1(t) = 156 + 0 * t + (1/2) * 32.2 * t^2
= 156 + 16.1 * t^2
h2(t) = 202 + 0 * t + (1/2) * 32.2 * t^2
= 202 + 16.1 * t^2
Therefore, the functions for the height of each ball as a function of time are:
h1(t) = 156 + 16.1 * t^2
h2(t) = 202 + 16.1 * t^2