PLEASE HELP!! A picnic basket falls out of a hot air balloon that is traveling horizontally at 14 m/s. The hot air balloon is
at an altitude of 250 m. Where does the picnic basket land relative to where it was dropped from?

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