College Algebra Word Problem

Question

A toy rocket is launched from the top of a building 123 feet tall at an initial velocity of 178 feet per second.
a) Give the function that describes the height of the rocket in terms of time t.
b) Determine the time at which the rocket reaches its maximum height, and the maximum height in feet.
c) For what time interval will the rocket be more than 545 feet above ground level?
d) After how many seconds will it hit the ground?
a) The function that describes the height of the rocket in terms of t is s left parenthesis t right parenthesis equals nothing .s(t)=
.

Answer 1

Hi Destiney, I will give you an overview, you work it out.

 

a) Basic function: h(x) = -16t² + vt + h₀, where t is time, v is initial velocity and h₀ is the original height above ground.

 

b) The basic equation is a parabola that opens down. Our equation is: h(x) = -16t² + 178t + 123

 

The time the rocket will reach its maximum height is given by: -b/2a, replacing a and b: -178/-32 = 5.625, or 5.625 seconds after the rocket has been launched it will reach its maximum height.

 

The maximum height of the rocket is given by: h(5.625) = -16 * (5.625)² + 173 * 5.625 + 123

 

c: To find when the rocket will be more than 545 feet above the ground level is given by:

 

545 = -16t² + 173t + 123

 

Solve this for t using the quadratic formula. You will get two values.

 

d: To find when the rocket will hit the ground, use the following equation:

 

0 = -16t² + 173t + 123

 

Solve this for t using the quadratic formula. You will get two values, one positive and one negative. Since time cannot be negative, the negative value can be discarded.

 

Let me know if you have questions.