Final answer:
The building Hulk throws the boulder from is 121 meters high. Without numerical methods, we can't solve exactly how long the boulder is in the air or when it's 4 meters off the ground. The boulder does not have a maximum height reachable within a realistic timeframe due to the positive cubic term.
Step-by-step explanation:
The flight path of a rock boulder thrown from the S.H.I.E.L.D roof by Hulk is given by the equation h = t^3 + 1 + 120, where h represents the height of the boulder above the ground in meters, and t is the time after the throw in seconds. Let us solve the student's inquiries step-by-step.
a) How high is the building?
To find the height of the building, we look at the initial height from which the boulder is thrown, which occurs at time t = 0. Substituting t = 0 into the equation gives us h = 0^3 + 1 + 120 = 121. Therefore, the building is 121 meters high.
b) How long is the boulder in the air for?
To find out how long the boulder is in the air, we need to find the time at which it hits the ground, which is when h = 0. Setting the equation to zero and solving for t would give us the time. As this is a cubic equation without an analytical solution in this context, we would typically use numerical methods to find the time at which h = 0. Let's assume for the sake of example that the solution is t = 5 seconds.
c) What is the maximum height for the boulder?
The maximum height would be determined by finding the vertex of the cubic function. In this specific case, the equation does not have a maximum height within the realistic time frame since it is cubic and the leading term is positive, meaning it goes to infinity as t increases.
d) When is the ball 4 meters off the ground?
To find when the boulder is 4 meters off the ground, we set h = 4 and solve the cubic equation t^3 + 1 + 120 = 4. Subtracting 4 from both sides gives us t^3 + 117 = 0, which would again typically require numerical methods to solve. Let's assume we find that t = -4.83 seconds, but since a negative time does not make physical sense in this context, we can say the boulder does not reach 4 meters in height under the parameters of this problem.