Answer to Question #249283 in Mechanics | Relativity for mikukumi292

Question

An object is thrown straight down from the top of a building at a speed of 43 m/s. It hits the ground with a speed of 87 m/s. a) How high is the building? b) How long was the object in the air? (note that there is an acceleration due to gravity).

Answer 1

(a) Write the equation for speed vs. height:

$$v_f^2=v_i^2+2gh,\\\space\\ h=\frac{v_f^2-v_i^2}{2g}=292\text{ m}.$$

(b) The time is

$$t=\frac{v_f-v_i}g=4.49\text{ s}.$$