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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?

User Nifle
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3 votes

Answer:


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.

User Tom Burman
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