Answer:
The boulder's maximum height is:
<u>a. Reaches a maximum height of 235.00 feet in 3.75 seconds</u>.
Step-by-step explanation:
The easiest way to solve the unknown is to replace the time in the given equation, with the values given in the answer, look for the highest value and check if the height value decreases as the time increases or decreases.
First the equation provided is taken:
- <u>h = -16t ^ 2 + 120t + 10
</u>
The time values in the options are 3.75 seconds and 7.5 seconds, therefore we proceed to replace this formula with those values:
- <u>h (3.75) = - 16 (3.75) ^ 2 + 120 (3.75) + 10 = 235
</u>
- h (7.5) = - 16 (7.5) ^ 2 + 120 (7.5) + 10 = 10
Since a higher height value is obtained with 3.75 seconds (235 feet), this time will be taken as appropriate, however, it is best to check that by using more time and less time, the height decreases from that value, so we will take two very close times: 3.74 seconds and 3.76 seconds:
- h (3.74) = - 16 (3.74) ^ 2 + 120 (3.74) + 10 = 234.9984
- h (3.76) = - 16 (3.76) ^ 2 + 120 (3.76) + 10 = 220.5884
<em>As you can see, if slightly higher or lower time values are taken, the height of the rock still decreases from 235 feet, so we can be sure that the time in which it reaches its maximum height is 3.75 seconds</em>.
