Find the Domain h=-16t^2+112t+704

Problem

h=−16*t2+112*t+704

Solution

1. Identify the type of function. The equation h=−16*t2+112*t+704 is a quadratic function representing the height of an object over time t

2. Determine the physical constraints. In the context of projectile motion, the time t must be non-negative (t≥0 and the height h must be non-negative (h≥0.

3. Set the height equation to zero to find when the object hits the ground.

−16*t2+112*t+704=0

4. Divide the entire equation by −16 to simplify the quadratic.

t2−7*t−44=0

5. Factor the quadratic equation.

(t−11)*(t+4)=0

6. Solve for t

t=11

t=−4

7. Select the interval that satisfies the physical constraints. Since time cannot be negative, we discard t=−4 The object is in the air from t=0 to t=11

Final Answer

Domain:[0,11]

Want more problems? Check here!