Question

A hot air balloon is ascending at the rate 42 m/s 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?

• A. t = 15s, u = - 58 m/s
• B. t = 10 s, u = - 58 m/s
• C. $t=\frac{8}{5}s,u=12.8m/s$
• D. t = 10 s, u = 58 m/s

Answer 1

The correct option is B

t = 10 s, u = - 58 m/s

Velocity of balloon is 42 m/s

s = -80m, a = -10 $m/s^2$

u = 42 m/s

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

$\Rightarrow -80=42t+\frac{1}{2}(-10)t^2$

$\Rightarrow -80=42t-5t^2$

$\Rightarrow 5t^2-42t-80=0$

t = 10, $\frac{-8}{5}$

$\therefore t=10s$

$v^2=u^2+2as$

$\Rightarrow v^2=(42{)}^2+2(-10\left)\right(-80)$

= 1764 + 1600

= 3364 m/s

$\Rightarrow v=\pm 58m/s$

$\therefore u=-58m/s$