Question

A ball is in a hot air balloon that starts from rest at t = 0 and accelerates upwards at 2m/s². After 10s, the ball is dropped from the balloon

The position time graph will be?

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

At t =10

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

= $0+\frac{1}{2}\times 2\left(100\right)$

= 100 m

$\therefore t=10,x=100m$

It will reach maximum displacement when

v = 0 ∴v = u + at

0 = 20 + (-10)t

0 = 20 - 10t

$\Rightarrow$t = 6

$\therefore$at t = 10 + 2, t = 12s, v = 0, x is maximum

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

$=20\left(2\right)+\frac{1}{2}(-10)\left(2^2\right)$

$=40+\frac{1}{2}(-10)4$

= 40 - 20 = 20 m

$\therefore$Displacement = 100 + 20 = 120 m

$\therefore$It will take another 2s to come back

$\therefore$at t = 14s, its displacement will be 100 as again.

$\therefore$correct option (a)