Final answer:
To find when the rocket's height is 87 feet using the equation h=195t−16t2, we insert 87 for h and solve the resulting quadratic equation. Calculating the discriminant and then applying the quadratic formula gives us the values of t when the rocket is 87 feet high.
Step-by-step explanation:
To find all values of t for which the rocket's height is 87 feet, we need to solve the equation h=195t−16t2 for t when h is 87. Inserting 87 for h results in the quadratic equation 87=195t−16t2, which simplifies to 16t2 - 195t + 87 = 0.
Using the quadratic formula t = (-b ± √(b2 - 4ac))/(2a), where a = 16, b = -195, and c = 87, enables us to determine the acceptable values of t.
The discriminant b2 - 4ac will determine how many real solutions there are. The quadratic equation with real coefficients will have either two different real solutions if the discriminant is positive, one real solution if it's zero, or no real solutions if it's negative.
After calculating the discriminant and if found positive, we need to evaluate the quadratic formula to find two possible times t when the rocket reaches a height of 87 feet. It is important to note that we are assuming the motion of the rocket is governed solely by the initial velocity and the acceleration due to gravity (neglecting air resistance), as indicated in the provided equation.