Question

Problem statement:The height after t seconds of a projectile that is launched upward with a velocity of 64 feet persecond from the top of a 45-foot building is given byℎ() = −162 + 64 + 45.a) When will the projectile attain a height of 85 feet?b) What is the maximum height attained by the projectile? When is the maximum heightattained?Round all answers to two decimal places.Questions student is to answer and/or complete:1. Please state in simple terms and in complete sentences your strategy for solving eachproblem.2. What method for solving quadratic equations did you choose? Why? Were there otheroptions available to you? If so, what were the other options?3. Is there more than one possible answer for each problem? Why or why not?

Answer 1

1. Strategy for solving each problem:
a) To find when the projectile attains a height of 85 feet, set the height equation ℎ() = 85 and solve for the time (). This involves solving a quadratic equation.
b) To determine the maximum height attained by the projectile, you’ll need to identify the vertex of the quadratic function. This vertex represents the peak of the projectile’s height, and its -coordinate will give the maximum height. You can also find the time at which the maximum height occurs.
2. Method for solving quadratic equations:
For both parts (a) and (b), the strategy involves setting the quadratic equation ℎ() = 85 (for part a) and finding the vertex of the quadratic function (for part b). You can use different methods to solve quadratic equations, such as factoring, completing the square, or using the quadratic formula. In this case, the quadratic formula might be the most straightforward approach due to the form of the equation.
3. Possible answers for each problem:
a) There might be two possible answers for part (a) since a projectile reaches a certain height while going up and then again while coming down. However, considering the context of the problem (attaining a height of 85 feet), there should be one time value relevant to the projectile reaching the specified height during its ascent.
b) For part (b), there will be only one maximum height attained by the projectile. The vertex of the parabolic trajectory represents this maximum height.

Remember, solving the quadratic equation in part (a) will provide the time(s) when the projectile reaches the height of 85 feet. Then, for part (b), analyzing the vertex of the quadratic function will yield the maximum height attained and the time at which this maximum height occurs.