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

Answer:

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

Step-by-step 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.