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?

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WaywardDelaney WaywardDelaney · Answer 1 · 2019-12-09T17:18:42+01:00

Answer:

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

Step-by-step 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 = [tex]\frac{\partial h}{\partial t}[/tex] = 0

Or, v = [tex]\frac{\partial h}{\partial t}[/tex] = 0

Now, v = [tex]\frac{\partial h}{\partial t}[/tex]

Or, v = [tex]\frac{\partial (-16t^{2}+160t)}{\partial t}[/tex]

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 = [tex]\frac{160}{32}[/tex]

∴ 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