Question

The height in feet of a projectile with an initial velocity of 224 feet per second and an initial height of 80 feet is a function of time t, in seconds, given by h(t) = -16t^2 + 224t + 80. Use algebra to find the time t when the projectile reaches its maximum height.

a) t = 7 seconds
b) t = 8 seconds
c) t = 9 seconds
d) t = 10 seconds

Answer 1

The time when the projectile reaches its maximum height is found using the vertex formula of a parabola, resulting in t = 7 seconds.

Step-by-step explanation:

To find the time t when the projectile reaches its maximum height, we need to determine the vertex of the parabola represented by the quadratic function h(t) = -16t2 + 224t + 80. The maximum height is achieved at the vertex of the parabola, and the time at which this occurs can be found using the formula t = -b/(2a), where a and b are the coefficients from the quadratic equation at²+ bt + c.

In this case, a = -16 and b = 224. Plugging these values into the formula gives us t = -224/(2 * -16) = 224/32 = 7 seconds. Therefore, the projectile reaches its maximum height at t = 7 seconds.