Question

A model rocket is launched with an initial upward velocity of 235 ft/s. The rocket's height h (In feet) after seconds is given by the following.h = 235t-167Find all values of t for which the rocket's height is 151 feet.Round your answer(s) to the nearest hundredth.(If there is more than one answer, use the "or" button.)

Answer 1

The equation relating the height,h and the time, t is expressed as

h = 235t - 16t^2

To find the values of t for which the rocket's height is 151 feet, we would substitute h = 151 into the equation and solve for h. Thus, we have

151 = 235t - 16t^2

16t^2 - 235t + 151 = 0

This is a quadratic equation. The general form of a quadratic equation is expressed as

ax^2 + bx + c = 0

By comparing the given equation with the general equation, we have

a = 16, b = - 235, c = 151

The formula for solving quadratic equations is expressed as

`\begin{gathered} x\text{ = }\frac{-\text{ b }\pm\sqrt[]{b^2\text{ - 4ac}}}{2a} \\ By\text{ substituting the values, we have} \\ x\text{ = }\frac{-\text{ - 235 }\pm\sqrt[]{(-235)^2-4(16\text{ }*151)}}{2\text{ }*16} \\ x\text{ = }\frac{235\text{ }\pm\sqrt[]{55225\text{ - 9664}}}{32} \\ x\text{ = }\frac{235\text{ }\pm\sqrt[]{45561}}{32} \\ x\text{ = }\frac{235\text{ }\pm213.45}{32} \\ x\text{ = }\frac{235\text{ + 213}.45}{32}\text{ or x = }\frac{235\text{ - 213}.45}{32} \\ x\text{ = }14.01\text{ or x = 0.67} \end{gathered}`

Repl

t = 14.01 or t = 0.67