Question

A ball is released from a hot air balloon moving downward with a velocity of -10.0 meters/second and a height of 1,000 meters. How long did it take the
ball to reach the surface of Earth? Given: g = -9.8 meters/second^2
A. 11.2 seconds
B. 12.1 seconds
C. 13.3 seconds
D. 13.5 seconds
E. 14.2 seconds

Answer 1

The equations starting from acceleration and taking the anti-derivative until you have position are shown below:
\[\textrm{a} =-9.8~ m/s^2 \]
\[\textrm{v} =-9.8t - 10 \] where the -10 is the initial velocity in the downward direction
\[x(t) = \frac{ 1 }{ 2 } (-9.8) t^2 - 10t + 1000 \] where +1000 is the initial position
you want to find the position at 0, so you solve the quadratic equation \[0 = \frac{ 1 }{ 2 } (-9.8) t^2 - 10t + 1000 \]
t=13.3