Analysing the Question:
We are given:
height of the hot air balloon (h) = 250 m
horizontal velocity of hot air balloon (p) = 14 m/s
Since the balloon had no vertical velocity, the basket will drop vertically at a velocity of 0 m/s and gain its velocity due to acceleration
whereas the horizontal velocity of the balloon is 14 m/s, so the basket will have a horizontal velocity of 14 m/s when falling
there will be no change in the horizontal velocity of the basket since there is no force against the horizontal velocity of the falling basket
Time taken by the basket to reach the ground:
from the last section, we deduced that:
initial vertical velocity (u) = 0 m/s
time taken by the basket to reach the ground (t) = t seconds
acceleration of the basket due to gravity (a) = 10 m/s²
from the second equation of motion:
h = ut + 1/2*at²
replacing the variables
250 = (0)t + 1/2 * (10)(t)²
250 = 5t²
t² = 50
t = √50
t = 5√2 seconds OR 7 seconds
Horizontal distance travelled by the basket:
Distance travelled = horizontal speed * time taken to reach the ground
Distance travelled = 14 * 7
Distance travelled = 98 m
