Question

An arrow is shot vertically upward from a platform 45 feet high at a rate of 168 ft/sec. Use the quadratic function

Answer 1

Answer:

5.3 s

Step-by-step explanation:

a) since the height is defined by a function, we can find the turning point of the quadratic , which is where the ball will have the highest point. The turning point is where the gradient is equal to zero so we differentiate first

$h(t) = -16t^{2} + 168t + 45\\h'(t)= -32t+168\\0=-32t+168\\t=5.3s$

Answer 2

Answer:

486 feet is reached after 5.25 seconds, which would round to 5.3

Step-by-step explanation:

Since a is negative, the parabola opens downward. The quadratic has a maximum. The equation is in general form, y=a$x^{2}$+bx+c, so use the formula −$\frac{b}{2a}$ to find the axis of symmetry.

The vertex is on the line t=5.25. The maximum height is reached after 5.25 seconds.

To find the maximum height, evaluate h(5.25).

h(5.25)=−16$t^{2}$$(5.25)^{2}$)+168(5.25)+45=486

The maximum height of 486 feet is reached after 5.25 seconds.