# The rate at which the velocity of a toy parachute decreases is given by 3h^2 - 14h. What is the height it should fall from so that its speed is 0 when it lands

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The expression that gives the rate at which the velocity of a toy parachute decreases is `3h^2 - 14h` .

`(dv)/(dh) = -(3h^2 - 14h)`

=> `dv = (14h - 3h^2) dh`

When the parachute is dropped the velocity is 0. As the parachute falls, its velocity increases at a rate 14h - 3h^2. The velocity after falling a distance h is

`int 14h - 3h^2 dh`

= `14h^2/2 - h^3`

= `7h^2 - h^3`

As the velocity of the parachute at touchdown is 0

`7h^2 - h^3 = 0`

=> `h^2(7 - h) = 0`

=> h = 7

**When the parachute is dropped from a height of 7 its velocity when it touches the ground is 0**.

Sorry, the question is: The rate at which the velocity of a toy parachute decreases is given by 3h^2 - 14h. What is the height it should fall from so that its speed is 0 when it lands.