Free Falling Objects A coin is dropped from a hot-air balloon that is 325 m abov

Question

Free Falling Objects A coin is dropped from a hot-air balloon that is 325 m above the ground and rising vertically at 11 m/s. For this problem use a coordinate system in which up is positive. The magnitude of the gravitational acceleration is g = 9.8m/s^2. (a) Find the maximum height, in meters, that the coin attains. (25%) (b) Find its height above the ground, in meters, 4.00 s after being released. (25%) (c) Find its velocity, in meters per second, 4.00 s after being released. (25%) (d) Find the time, in seconds, that it takes the coin to hit the ground. (25%)

Explanation / Answer

a] Initial velocity = u = 11 m/s

at the highest point, v = 0 m/s

h = [v2 - u2]/2a

=> h = - [-112]/(2 x 9.8) = 6.173m

so the maximum altitude will be: H = 325 + 6.173 = 331.173m

b] h = ut + (1/2)at2

=> h = (11)(4) - (1/2)(9.8)(4)2 = - 34.4m

so, height from the ground will be: H = 325 - 34.4 = 290.6 m

c] v = u + at

=> v = 11 - 9.8(4) = - 28.2 m/s [downwards]

d]

v = u + at

0 = 11 - 9.8t

=> t = 1.122s

at height H = 331.173m, v = 0m/s

so, velocity V at the ground will be:

(1/2)mV2 = mgH

=> V = 80.567 m/s

now, V = u + at'

=> 80.567 = 0 + 9.8t'

=> t' = 8.22s

therefore, total time it takes for the coin to come down = T = t + t' = 1.122 + 8.22 = 9.343s.

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