Question

Algebra 2
Scott launches a model rocket from ground level. The rocket's height h in meters is given by the equation h = -4.9t sq + 56t, where t is the time in seconds after the launch.
a) what is the maxium height the rocket will reach?
b) how long after it is launched will the rocket reach its maxium height?
c) Scott stands on a stool that is 3 meters off the ground to launch the rocket, what is the new height equation? What is the new max height?

Answer 1

hey is this a calc/derivative problem?

Answer 2

or are you supposed to be solving it in a different way

Answer 3

you can do this with the first derivative

Answer 4

you want to know when the rate of change of the height is zero, so you take the first derivative

Answer 5

1. h = -4.9t^2 + 56t
2. dh/dt = -4.9*2*t + 56

Answer 6

3. 56 -9.8t

Answer 7

there will be a maximum when that rate is zero

Answer 8

so 56 = 9.8t

Answer 9

t - 56/9.8

Answer 10

errr t = 56/9.8

Answer 11

= 560/98 = 280/49 = 40/7

Answer 12

so at 40/7 seconds, it will reach its highest point

Answer 13

so 40/7 seconds is the correct answer for (B). if you put that back into original height equation, you will have the answer to A.

Answer 14

the answer to C is just 3 meters plus the answer to A

Answer 15

since the rocket still peaks after the same amount of time - just three meters higher

Answer 16

let me know if you were supposed to do this in a different way (eg. graphing)

Answer 17

can you do it graphing? That would be a great help to have both methods.