Question

A stone is dropped from the roof of a building; 1.90 s after that, a second stone is thrown straight down with an initial speed of 27.0 m/s , and the two stones land at the same time.

A) How long did it take the first stone to reach the ground?

B) How high is the building?

c) What are the speeds of the two stones just before they hit the ground? Enter your answers numerically separated by a comma.

Answer 1

Given,

t = 1.9 s ; vi = 27 m/s

a)The distance travelled will be same for both

1/2 x9.8 t^2 = v0 (t - 1.9) + 1/2 x 9.8 x (t - 1.9)^2

4.9 t^2 = v0t - 1.9 v0 + 4.9 (t^2 + 3.61 - 3.8 t)

4.9 t^2 = v0t - 1.9 v0 + 4.9 t^2 + 17.7 - 18.62 t

put value of v0

0 = 27 t - 51.3 + 17.7 - 18.62 t

t = 33.6/8.38 = 3.94 s

Hence, t = 3.94 s

b)y = 1/2 gt^2

y = 0.5 x 9.81 x 3.94^2 = 76.14 m

Hence, y = 76.14 m

c)v = u + at

v = gt

v = 9.8 x 3.94 = 38.61 m/s

Hence, v = 38.61 m/s

v' = v0 + at

v' = 27 + 9.81 x (3.94 - 1.9) = 47.01 m/s

Hence, v' = 47.01 m/s