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
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.