Question

if h=-16t ²+160t represents the height of a rocket in T seconds after it was fired when will the rocket hit the ground?

Answer 1

The time after which the rocket hit the ground is 5 seconds

Explanation:

Given as :

The distance of the cover by rocket at the height h = - 16 t² + 160 t

Let the time after which rocket hit the ground = T seconds

Now, When the rocket hits the ground, then at that time, the velocity of the rocket becomes zero.

I.e velocity =
`(\partial h)/(\partial t)` = 0

Or, v =
`(\partial h)/(\partial t)` = 0

Now, v =
`(\partial h)/(\partial t)`

Or, v =
`(\partial (-16t^(2)+160t))/(\partial t)`

or, v = - 32 t + 160

Now, ∵ velocity of rocket after reaching the ground becomes zero

So, v = - 32 t + 160 = 0

Or, 32 t = 160

Or, t =
`(160)/(32)`

∴ t = 5 sec

So, The time after which the rocket hit the ground = 5 sec

Hence The time after which the rocket hit the ground is 5 seconds answer