The height h in a ball at t seconds after being tossed upwards is given by the function h(t)=84-16t ²?

Question

The height h in a ball at t seconds after being tossed upwards is given by the function h(t)=84-16t ²?

Answer 1

h(t) = 84 -16t^2

at initial time t=0, the ball is at height 84 with initial velocity=0. It's not tossed upwards with this equation. It's dropped, but without being tossed downward either.

it reaches a maximum height when h'(t) = 0 = -16t, at time t=0, at height = 84, after that it goes down to lower heights.

It reaches ground level, h=0, when 16t^2 = 84 feet

t^2 = 84/16 = 42/8 =21/4

t = sqr(21/4) = (1/2)sqr21 = about 2.3 seconds, the time it takes gravity to pull the ball 84 feet down

the term -16t^2 indicates deceleration due to gravity at 32 feet per second per second

You need a t term if the ball was tossed upwards with any velocity > 0. Vot is missing where the coefficient of a linear t term is the initial velocity. With just 84-t^2, initial velocity is zero