Motion in One Dimension Problem - 5

Description:

Question

A hot air balloon is ascending at the rate of 12 ms^-1 and is 80 m above the ground when a package is dropped over the side

a. How long does the package take to reach the ground?

b. With what speed does it hit the ground?

Solution

a. When a ball is dropped, its initial velocity is considered as zero.

But in this case initial velocity is not zero because the package which is dropped was placed inside the balloon which was moving with 12 ms^-1, so the package also has an initial velocity of u = 12

By applying kinematic equation −

S = ut + 1/2 at²

Putting the given values −

-80 = 12t - 1/2 10t²

5t² - 12t - 80 = 0

t = 12 ± √144 - 4 × 5(-80)/2 × 5

t = 12 ± √1744/10 ≈ 12 ± 42/10

t = 54/10 = 5.45

Time taken by the package to reach the ground is 5.45 sec

b. To calculate speed, we use kinematic equation −

v² = u² + 2as

v² = 12² + 2 × (-10)(-80)

v² = 144 + 1600 = 1744

v ≈ 42ms^-1

The package hit the ground with a speed of 42 ms^-1