an algebra word problem

Question

you launch a model rocket from ground level with an initial velocity of 95 feet per second.  After how many seconds will the rocket have and altitude of 114 feet?

Answer 1

Lisa,

        I'm going to assume that this launch takes place in the earths gravitational field g=-32.2ft/sec².

 

so d=V₀t-1/2gt² where d= distance traveled in the y direction, V₀= the initial speed =95 ft/sec. This equation describes the position of the rocked as a function of time. To find out when (t=?) the rocket's altitude is 114 ft you set d=114 and solve the resulting quadratic equation (114=95t-16t²) for the values of t. There will be two solutions the smallest one is the one you want. The larger one represent the time it take to reach 114 ft on the way down. I got t=1.6693 sec.

 

Hope this helps

 

Jim

Answer 2

Assuming there's no air resistance, this can be solved by setting up an function. You know that the the rocket travels 95 feet in 1 second, 190 in 2, and so on. This can be expressed as the linear equation y=95x, with x representing the number of seconds that has passed and y representing the altitude at a given time. You already know the altitude (y) must be 114 feet. Plugging this information in, all you have to do is solve for x. So,

 

y=95x

114=95x

114/95=x

1.2=x

 

The rocket will take 1.2 seconds to reach an altitude of 114 feet. 

 

To check, plug 1.2 into the original equation as x, and you should get 114.

 

y=95x

y=95(1.2)

y=114