can you give me a solution?

Question

 A hot-air balloon is ascending at the rate of 10 kph. If a bomb is dropped from the balloon such that it takes 8 seconds to reach the ground, determine the balloon’s altitude when the bomb was released. (Ans. 291.6 m)

Answer 1

Standard acceleration due to gravity is -9.8 m/s². Let's change that 10 kph into meters per second, since that's what we'll use to work with gravity.

 

(10 kilometers / 1 hour) × (1000 meters / 1 kilometer) × (1 hour / 60 minutes) × (1 minute / 60 seconds) = (10×1000) / (60×60) m/s = 10000/3600 m/s = 25/9 m/s. This is the initial velocity of the bomb.

 

 

Use this equation for free-fall, where v_i = initial velocity, t = time, d = distance, and a = acceleration due to gravity:

 

d = v_it + 1/2(a)(t²)

 

 

For you, v_i = 25/9, a = -9.8, and t = 8. Plug in and solve for d:

 

d = (25/9)(8) + 1/2(-9.8)(8²)

d = 22.22 + (-4.9)(64)

d = 22.22 - 313.6

d = -291.4

 

 

That means the bomb has fallen downwards 291.4 meters. That discrepancy in the answers is due to rounding.