Question

a balloon which is ascending at the rate of 12 m per second is 30.4 m above the ground when a stone is dropped after what time the stone will reach the ground

Answer 1

4 answers · Physics 

Answers

Use the following equation . 

d = vi * t + ½ * a * t^2, d represents the balloon’s vertical displacement. 
Vertical displacement = final height – initial height = 0 – 30.4 = -30.4 m 
vi = 12 m/s, a = -9.8 m/s^2 

-31.4 = 12 * t + ½ * -9.8 * t^2 
4.9 * t^2 – 12 * t – 31.4 = 0 
t = [12 ± √(144 – 4 * 4.9 * 31.4)] ÷ 9.8 
t = [12 ± √759.44] ÷ 9.8 
t = [12 + √759.44] ÷ 9.8 = 4.036524384 seconds 

To check this answer, let’s round it to 4.0365 seconds. 

-31.4 = 12 * 4.0365 + ½ * -9.8 * 4.0365^2 = -31.39932803 
Since I rounded it, this proves that it is correct.

Answer 2

Answer:

step by step

V=U+at

0=12-10t (minus is used because it oppose the gravity)

10t=12

t=12/10

t=1.2seconds

distance coverde by the stone

v*2=u*2+2as

s=distance =h,a=g

so it become

v*2=u*2+2gh

(0)*2=(12)*2-20h( 2*(-10)=-20)

20h=12*2

h=12*12/2*10

h=36/5=7.2m Now, when the stone is dropped before it was rest so initial is zero and a=g

so,

h=ut+1/2gt*2

now as u=0 it becomes

h=1/2gt*2 so. 7.2=1/2*10*t*2

t*2= 7.2*2/10

t=under root 14.4/10

t=under root 144/100

t=12/10 stone at height=30.4+7.2=37.6m

h=1/2gt*2 (u=0,a=g)

37.2=1/2*10*t*2

t=under root 37.6*2/10 then in denominator we can write 10=2*5 so

t=under root37.6/5(2 and 2 is both cancel)

t=under root 7.52

t=2.7(approx)

total time taken =2.7+1.2=4 seconds