Tyler throws his algebra 2 book

Question

tyler throws his allgebra 2 book upward wile standing on the rooftop of a building that is 20 feet high the math book has an inital velocity of 28 feet/second the motion of the book is molded by the equation h=-16t^2+40t+20

Answer 1

if the initial velocity is 28 feet per second

the equation that models its height is: h(t) = -16t^2 +28t +20

NOT h(t)=-16t^2 +40t + 20. this equation has an initial velocity of 40 feet per second

1st equation has a maximum height when -32t +28 = 0, at time t=28/32 =7/8th of a second

and max height at h(7/8) = -16(7/8)^2 +28(7/8) +20 = -49/4 +49/2+20= 32 1/2 feet high

it hits the ground when h(t)=0 = -16t^2 +28t +20 = 0

when 4t^2 -7t-5 = 0

t= 7/8 +(1/8)sqr(49+48)

= (7+sqr97)/8 = about 2 seconds

2nd equation has maximum height when -32t+40=0 at time t= 40/32 =5/4 =1.25 seconds

and max height at h(5/4)= -16(5/4)^2 +40(5/4) +20 = 45 feet high

it hits the ground when h(t)=0 =-16t^2 +40t +20

when 4t^2 -10t-5=0

t= 10/8 + (1/8)sqr(100+80)

t = about 5/4+5/3= 35/12 = almost 3 seconds

the -16t^2 term reflects the effect of gravity at 32 feet per second per second deceleration, at sea level. It's a close approximation. It varies by altitude and latitude. In Chicago, g=9.8026 with altitude = 179 meters above sea level. for meters the equation is h(t) =-9.8026t^2/2 +vot +ho where ho= initial height, vo=initial velocity and -9.8026/2= -4.9013 = g/2 where g= deceleration due to gravity.