after solving a difficult physics problem, an excited student throws his book st

Question

after solving a difficult physics problem, an excited student throws his book straight up. it leaves his hand at 3.4m/s from 1.5 m above ground. how much time does it take until the book hits the floor? after solving a difficult physics problem, an excited student throws his book straight up. it leaves his hand at 3.4m/s from 1.5 m above ground. how much time does it take until the book hits the floor? after solving a difficult physics problem, an excited student throws his book straight up. it leaves his hand at 3.4m/s from 1.5 m above ground. how much time does it take until the book hits the floor?

Explanation / Answer

Take vertically up direction as positive

vi = 3.4 m/s

a = -9.8 m/s^2 (negative because it is directed downward)

d = -1.5 m (negative because net displacement of book is downward)

use:

d = vi*t + 0.5*a*t^2

-1.5 = 3.4*t + 0.5*(-9.8)*t^2

-1.5 = 3.4*t - 4.9*t^2

4.9*t^2 - 3.4*t -1.5 = 0

This is quadratic equation (ax^2+bx+c=0)

a = 4.9

b = -3.4

c = -1.5

Roots can be found by

t = {-b + sqrt(b^2-4*a*c)}/2a

t = {-b - sqrt(b^2-4*a*c)}/2a

b^2-4*a*c = 40.96

roots are :

t = 1 and t = -0.3061

since t can't be negative, the possible value of t is

t = 1

Answer: 1 s

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