Question

The height above the surface of the Earth​ (in meters) of a rock thrown into the air at 10​ m/s after x seconds is given by f(x)=−9.8x2+10x+1.5. On the surface of the​ moon, the height is given by g(x)=−1.6x2+10x+1.5. How much higher does the rock travel on the moon than on​ Earth? The rock travels about __ ​meter(s) higher on the moon than on Earth.

Answer 1

Rock travels about 8.2x²meters higher on the moon than on the Earth.

Explanation:

Expression showing the height of a rock thrown into the air at Earth is,

f(x) = -9.8x² + 10x + 1.5

Similarly, expression showing the height of rock thrown on the moon is,

g(x) = -1.6x² + 10x + 1.5

Difference in the height of the rock thrown on moon = g(x) - f(x)

= (-1.6x² + 10x + 1.5) - ( -9.8x² + 10x + 1.5)

= -1.6x² + 9.8x² + 10x - 10x + 1.5 - 1.5

= 8.2x²

Therefore, rock travels about 8.2x²meters higher on the moon than on the Earth.