Question

A balloon is rising with a velocity of 2 m/s when a bag of sand is released. If the height at the time of release is 120 m. How long does it take the bag of sand to reach the ground?​

Answer 1

Given :

Velocity of ball = 2m/s

Height from the ground = 120m

To Find :

Time taken by sand bag to reach the ground.

Solution :

★ Let’s assume ground to be a reference and upward direction as positive.

Second equation of kinematics is given by

• $\underline{\boxed{\bf{\purple{x=x_o+ut+\dfrac{1}{2}at^2}}}}$

where,

x denotes final position

xo denotes initial position

u denotes initial velocity

t denotes time taken to strike the ground

a denotes acceleration

By substituting the given values;

$:\implies\sf\:x=x_o+ut+\dfrac{1}{2}at^2$

$:\implies\sf\:0=120+2t+\dfrac{1}{2}(-10)t^2$

• Negative sign of g shows downward direction!

$:\implies\sf\:0=120+2t-5t^2$

$:\implies\sf\:5t^2-2t-120=0$

On solving we get,

$:\implies\:\underline{\boxed{\bf{\orange{t=5.1\ s}}}}$