Question

A stone is dropped from a balloon at an altitude of 300 m . how long the stine will reach the ground if a ballon is ascending with a velocity of 5 m (b) descending with a velocity of 5 m

Answer 1

Given :

A stone is dropped from a balloon at an altitude of 300 m .

To Find :

how long the stine will reach the ground if a ballon is ascending with a velocity of 5 m (b) descending with a velocity of 5 m

Solution:

A stone is dropped from a balloon at an altitude of 300 m

a) how long the stone will reach the ground if a balloon is ascending with a velocity of 5 m

Initial velocity of stone upward u= 5m/s

By using equation of motion :

$s=ut+\frac{1}{2}gt^2$

Here displacement is in negative y direction and initially it was going upwards s=-300

$g=-10m/s^2$

So,$-300=5t+\frac{1}{2}(-10)t^2$

$-300=5t-5t^2\\-60=t-t^2\\t^2-t-60=0\\t=\frac{1}{2}-\frac{\sqrt{241}}{2},\frac{1}{2}+\frac{\sqrt{241}}{2}\\t=-7.262,8.26$

Since time cannot be negative

Hence the stone will reach the ground in 8.26 seconds

b) how long the stone will reach the ground if a balloon is descending with a velocity of 5 m

u = 5 m/s

$g = 10 m/s^2$

s=300

Using equation of motion

$s=ut+\frac{1}{2}gt^2$

$300=5t+\frac{1}{2}(10)t^2\\300=5t+5t^2\\60=t+t^2\\t^2+t-60=0\\t=-\frac{1}{2}-\frac{\sqrt{241}}{2},-\frac{1}{2}+\frac{\sqrt{241}}{2}\\t=−8.26,7.26$

Since time cannot be negative

Hence the stone will reach the ground in 7.26 seconds

Answer 2

Answer:

Given :

A stone is dropped from a balloon at an altitude of 300 m .

To Find :

how long the stine will reach the ground if a ballon is ascending with a velocity of 5 m (b) descending with a velocity of 5 m

Solution:

A stone is dropped from a balloon at an altitude of 300 m

a) how long the stone will reach the ground if a balloon is ascending with a velocity of 5 m

Initial velocity of stone upward u= 5m/s

By using equation of motion :

s=ut+\frac{1}{2}gt^2s=ut+21gt2

Here displacement is in negative y direction and initially it was going upwards s=-300

g=-10m/s^2g=−10m/s2

So,-300=5t+\frac{1}{2}(-10)t^2−300=5t+21(−10)t2

\begin{lgathered}-300=5t-5t^2\\-60=t-t^2\\t^2-t-60=0\\t=\frac{1}{2}-\frac{\sqrt{241}}{2},\frac{1}{2}+\frac{\sqrt{241}}{2}\\t=-7.262,8.26\end{lgathered}−300=5t−5t2−60=t−t2t2−t−60=0t=21−2241,21+2241t=−7.262,8.26

Since time cannot be negative

Hence the stone will reach the ground in 8.26 seconds

b) how long the stone will reach the ground if a balloon is descending with a velocity of 5 m

u = 5 m/s

g = 10 m/s^2g=10m/s2

s=300

Using equation of motion

s=ut+\frac{1}{2}gt^2s=ut+21gt2



Since time cannot be negative

Hence the stone will reach the ground in 7.26 seconds