Sharon and haliegh are playing a game together. Haleigh stand as still as she can while Sharon throws a balloon at her from her roof. The balloon Sharon throws can be represented by the function b(t) and haleigh can be presented by the function h(t)
The function representing the balloon Sharon throws can be represented as follows:
b(t) = 9.8t^2 + v0t + h0
Where:
- t is the time in seconds since the balloon was thrown
- v0 is the initial velocity of the balloon
- h0 is the initial height of the balloon when it was thrown
The function representing Haleigh standing still can be represented as follows:
h(t) = h0
Where:
- t is the time in seconds since the game started
- h0 is the initial height at which Haleigh is standing
The objective of the game is for Sharon to hit Haleigh with the balloon by calculating when the two functions intersect, i.e., when b(t) = h(t). By solving the equation 9.8t^2 + v0t + h0 = h0, Sharon can determine the time at which the balloon hits Haleigh.
Of course, this game should be played with caution to ensure that Haleigh is not harmed, and safety precautions should be taken to prevent any accidents.