Question

1. A stone is thrown straight downward with initial speed of 4.1 m/s from a height of 86 m. What is the time it takes to reach the ground?

2. You drop a stone into a 300 meter deep well. How long after you will hear the sound of hitting? Sound velocity is given 334 m/s.

3. You throw a stone vertically upward from the roof of an 39 m tall building with a velocity of 54 m/s. How long after the stone will land the ground? [Assume g=10m/s2]

Answer 1

1)

s= ut + 1/2*g*t^2

86 = 4.1*t +0.5*10*t^2

from here t≈3.75751 sec

2) time taken by stone to reach at the bottom

s= ut+1/2*g*t^2

300 = 0 +0.5*10*t^2

t= sqrt( 2*300/ 10) = 7.74596669 sec

now sound will genrate so time taken by sound to reach to you t' = distance /velocity= 300/334 = 0.898203593 s

so total time = 7.74596669+0.898203593 = 8.64417028 s  

so after this much time u can hear sound of dropped stone

3)

time taken to reach maximum height

v= u +gt

0 = 54 -10*t1

t1 = 54/10= 5.4 sec

same time it will take to reach same height t2 = 5.4 sec

now this will travel 39 m to recah the ground

s= ut+1/2*g*t^2

39 = 54*t+0.5*10*t^2

from here t3 =0.6794 sec

total time = t1+t2+t3 =  5.4+ 5.4+0.6794 = 11.4794 s