Ball thrown in the air, max height

Question

A ball is thrown vertically upward from the ground with an initial velocity of 109 ft/sec. Use the quadratic function h(t)=−16t^2+109t to find how long it will take for the ball to reach its maximum height, and then find the maximum height. Round your answers to the nearest tenth

Answer 1

This Physics question has its height related to time by a parabola

with equation:

s = 1/2*a*t^2 + v0*t + s0, where s is the height,

s0 is the starting height,

v0 is its starting velocity = 109 ft/s

a is the acceleration of gravity, which is -16 ft/s every second.

How long will it take to reach the peak?

v = a*t + v0 (its velocity is acceleration of gravity * time + v0)

v will slow down from 109 ft/s to 0 ft/s,

slowing down at 16 ft/s every s:

t (s) --- v (m/s)

0 --------- 109

1 ----------- 93

2 ----------- 77

3 ----------- 61

4 ----------- 45

5 ----------- 29

6 ----------- 13

... before 7 s, it will hit the ground. Exact calculation

t = 109 ft/s / 16 ft/s/s

t = 6.81 s.

But, v0 was only given to 3 sig figs (109), and a to 2 sig figs (16).

We must use the minimum significant figures

of all numbers in this calculation...

t = 6.8 s, this is the answer to the problem.

Hope that helps.