Question

A baseball is hit so its height above ground is given by the following equation h = -16t² +100t + 5, where h is the height in feet and t is the time in seconds after it is hit. How long does it take the baseball to reach its highest point?

Answer 1

To find out how long it takes for a baseball to reach its highest point based on the given quadratic equation, apply the formula t = -b/(2a). Using the coefficients from the equation h = -16t² +100t + 5, the time is calculated to be 3.125 seconds.

Step-by-step explanation:

The student's question asks how long it takes for a baseball to reach its highest point when its height above ground is given by the quadratic equation

h = -16t² +100t + 5, where h is height in feet and t is time in seconds. To find the time when the baseball reaches its highest point, we need to find the vertex of the parabolic function, which gives the maximum height for a projectile motion.

We can calculate this by using the formula

t = -b/(2a), where a is the coefficient of the t² term, and b is the coefficient of the t term in the equation. In this case, a is -16, and b is 100. Plugging these into the formula, we get

t = -100/(2*-16), which simplifies to

t = 3.125 seconds. Therefore, it takes the baseball 3.125 seconds to reach its highest point.