Question

The height of a firework shot upward from the ground with the initial velocity of 10meters per second is represented by the function h(t) = - 16t2 + 4t How long did it take the firework to reach the ground

Answer 1

0.375 seconds

Explanation:

In simple terms, to find the time it took to reach the ground, we need to find t from the equation.

If we differentiate h with respect to t we will get the velocity with which the fireworks is moving at.

`h(t) = - 16t^2 + 4t.\\dh/dt =-32t +4`

We can now equate this to its velocity and solve for t

10 = -32t +4

t = 0.1875 ( time cannot be negative in value, so we ignore the negative sign)

Therefore, the time it took the fireworks to reach the ground is = 2 x 0.1875= 0.375 seconds.

(We need to account for the fact that the fireworks went up and came down)