## A rocket is shot straight into the air at an initial velocity of 70 feet/second. The height of the rocket after t seconds is repre

Question

A rocket is shot straight into the air at an initial velocity of 70 feet/second. The height of the rocket after t seconds is represented by the formula h=70t−5t^2. What is the maximum height the rocket reaches?

in progress 0
31 mins 2023-01-23T22:25:44+00:00 1 Answer 0 views 0

## Answer ( 1 )

1. By making use of properties of quadratic equations, we conclude that the maximum height of the rocket is 245 feet.

### What is the maximum height of the rocket?

In this problem we must obtain the maximum height reached by the rocket and based on the quadratic equation described in the statement. There is an algebraic approach to get such information quickly. First, we modify the polynomial into an implicit form:
– 5 · t² + 70 · t – h = 0
Graphically speaking, quadratic equations are parabolae and, in particular, the maximum height of the rocket is part of the vertex of the parabola. Then, the discriminant of the quadratic equation is:
70² – 4 · (- 5) · (- h) = 0
4900 – 20 · h = 0
h = 245
By making use of properties of quadratic equations, we conclude that the maximum height of the rocket is 245 feet.