Question

A stone is thrown vertically into the air at an initial velocity of 79 ​ft/s. On a different​ planet, the height s​ (in feet) of the stone above the ground after t seconds is sequals79tminus3t squared and on Earth it is sequals79tminus16t squared. How much higher will the stone travel on the other planet than on​ Earth?

Answer 1

`13t^2` feet higher the stone will travel on the other plant than on Earth.

Explanation:

Initial velocity of the stone thrown vertically = 79 ft/s

It is given that:

Height attained on a different planet with time
`t`:

`s_p = 79t -3t^2`

Height attained on Earth with time
`t`:

`s_e = 79t -16t^2`

If we have a look at the values of
`s_p\text{ and }s_e`, it can be clearly seen that the part
`79t` is common in both of them and some values are subtracted from it.

The values subtracted are
`3t^2\text{ and } 16t^2` respectively.

`t^2` can never be negative because it is time value.

So, coefficient of
`t^2` will decide which is larger value that is subtracted from the common part i.e.
`79t`.

Clearly,
`3t^2\text{ and } 16t^2` have
`16t^2` are the larger value, hence
`s_e < s_p`.

So, difference between the height obtained:

`s_p - s_e = 79t - 3t^2 - (79t - 16t^2)\\\Rightarrow 79t -3t^2 - 79t + 16t^2\\\Rightarrow 13t^2`

So,
`13t^2` feet higher the stone will travel on the other plant than on Earth.