Question

A stone is thrown vertically upward from a platform that is 20 feet high at a rate of 160 ft/sec. Using the quadratic function h(t) = -16t^2+160t+20 to find how long will it take the stone to reach its maximum height, and then find the maximum height. Round your answer to the nearest tenth

Answer 1

Answer:

5 seconds

1220 ft

Step-by-step explanation:

Step 1: Know when the stone reaches the maximum height

We know the maximum or minimum height of a parabola is at the vertex so we need to find the vertex

Step 2: Calculate the vertex

The t coordinate of the vertex can be calculated with $\frac{-b}{2a}$

b = 160

a = 16

$t=\frac{-(160)}{2(-16)}\\t=\frac{-160}{-32}\\t=5$

Step 3: We know the t coordinate we can find the height at that time

$h_{(t)} =-16(5)^{2} +160(5)+20\\h_{(t)}=16(25)+ (800)+20\\h_{(t)}=400+ 800+20\\h_{(t)}=1220$

Therefore the stone reaches its maximum height of 1220 ft in 5 secs