1. trajectory flight

Question is:

given the equation for fireworks: f(x) = 24.5t - 4.9t^2

what velocity does the rocket travel at its maximum height?
what time would the fuse timer need to be set at to have the rocket explode at maximum height?
at what height would the rocket explode at with the minimum fuse timer setting?

I solved for x=a and found that m=24.5 - 9.8a
I think that this is the velocity at the maximum height where a = the max height but I am lost as to how to finish the second part of the question.

2. Originally Posted by conman
Question is:

given the equation for fireworks: f(x) = 24.5t - 4.9t^2

what velocity does the rocket travel at its maximum height?
what time would the fuse timer need to be set at to have the rocket explode at maximum height?
at what height would the rocket explode at with the minimum fuse timer setting?

I solved for x=a and found that m=24.5 - 9.8a
I think that this is the velocity at the maximum height where a = the max height but I am lost as to how to finish the second part of the question.
This is very confused, but let us assume that f(t) represents the height
at time t, and we are discussing 1 dimensional motion.

When the rocket is at its maximum height its velocity is 0.

The velocity is obtained by differentiating the equation for the height, so
the velocity is:

df/dt = 24.5 - 9.8t.

At the maximum height df/dt=0, so this occurs when:

24.5 - 9.8t = 0,

or:

t = 24.5/9.8 ~= 2.5 seconds

So the fuse would have to be set to 2.5 seconds to have the rocket explode
at its maximum height.

The height at which the rocket explodes is:

f(2.5) = 24.5*2.5 - 4.9*2.5^2 = 30.625 metres.

RonL