TQ 2-81

Given:

V₀ = -2.00 m/s 

 y₀ = 45.0 m

y = 0 m

(a) Find : t - ? 

y = y₀ + V₀ t - 1/2 g t ²

0 = y₀ + V₀ t - 1/2 g t ²

1/2 g t ² - V₀ t -  y₀ = 0

This is a quadratic equation with the following solution:

t = [ V₀ +/- ( V₀² + 2 g y₀)^1/2]/g

The time we are looking for must be positive:

t = 2.83 s

(b) Find : V - ?

V = V₀ - g t

V = (-2.00 m/s) - (9.80 m/s²)(2.83 s) = -29.7 m/s