Answer:
A) t = 7.25 sec
B) 45.92 m above the cliff and 85.92 m counting from ground level
C) about 0.6 m/s
D) The only acceleration is always that of gravity : 9.8 m/s^2
Step-by-step explanation:
The kinematic equation for the position as a function of time is:
y = 40 + 30 * t - (g/2) t^2
The total time the balloon was in the air is calculated for when the final position is y = 0 (when it touches the ground), that is:
0 = 40 + 30 * t - (g/2) t^2
0 = 40 +30 t - 4.9 t^2
which can be solved for "t" using the quadratic formula, and which renders two different times "t", of which we pick the positive answer: t = 7.25 sec.
For the maximum height, we estimate the time it takes for the balloon to reach the maximum height at which the velocity is zero (changes direction of motion):
vf = vi - g * t
0 = 30 - 9.8 * t
t = 30 / 9.8 = 3.06 seconds
Now we use this value in our position equation and get:
ymax = 40 + 30 (3.06) - 4.9 (3.06)^2
ymax = 85.92 m (from ground level
Therefore, from the cliff (that is at 40 m height) the height is 85.92 - 40 = 45.92 m.
The velocity of the balloon at t = 3 seconds can be calculated with the velocity expression we have been using:
v(t) = vi - g * t
v(3) = 30 - 9.8 (3) = 0.6 m/s
The only acceleration acting on the balloon is always the acceleration due to gravity (g = 9.8 m/s^2)