A ball is thrown into the air from a height of 4 feet at time t = 0. The function that models this situation is
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Given formula : formula t = −0.0035a + g, where t is the atmospheric temperature in degrees Fahrenheit, a is the altitude in feet and g is the ground temperature in degrees Fahrenheit.
To find: 1) If the atmospheric temperature is −25.4 °F and the ground temperature is 60°F, what is the altitude?
2) The equation for a is a = .
Solution: 1) We have atmospheric temperature(t) =−25.4 °F, and
ground temperature(g) =60°F.
Plugging values of t and g in given formula t = −0.0035a + g, we get
-25.4 = −0.0035a + 60.
Subtracting 60 from both sides, we get
-25.4 - 60 = −0.0035a + 60-60
-85.4 = −0.0035a.
Dividing both sides by -0.0035, we get
-85.4/-0.0035 = −0.0035a/-0.0035.
24400 = a
Therefore, if the atmospheric temperature is −25.4 °F and the ground temperature is 60°F, the altitude is 24400 feet.
2) We need to solve equation for a in this part.
We have
t = −0.0035a + g
Subtracting g from both sides, we get
t -g = −0.0035a + g-g
t-g = −0.0035a
Dividing both sides by −0.0035, we get
(t-g)/-0.0035 = −0.0035a/-0.0035
Distributing minus sign on the top, we get
.
Therefore, the equation for a is a =(g-t)/0.0035.