The acceleration due to gravity on Earth is 32 ft/sec2. A tomato is dropped from

Question

The acceleration due to gravity on Earth is 32 ft/sec2. A tomato is dropped from 100 feet above the ground. Give units in your answers. At what speed does the tomato hit the ground? How long does it take for the tomato to travel the last 10 feet? Give your answer as a decimal approximation with units. Suppose you look out the window of a skyscraper and see someone throw a tomato downward from above your window. Your window is at a height of 450 feet above the ground. The tomato passes your window after 2 seconds and hits the ground 5 seconds after it was thrown. Neglect air resistance, and give units in your answers. Find the velocity (with the positive direction pointing up) at which the tomato was thrown. Find the height from which the tomato was thrown. (Another tomato/skyscraper problem.) You are looking out your window in a skyscraper, and again your window is at a height of 450 feet above the ground. This time, however, you know that the tomato was dropped (so v0 = 0), but you did not see it dropped so you do not know when it was dropped. You measure that it takes exactly 2 seconds from the time the tomato passes your window until it hits the ground. From what height did it fall? Give your answer as a decimal approximation with units.

Explanation / Answer

1)
a) v^2-u^2 = 2*g*h

v^2 - 0 ^2 = 2*g*h

v = sqrt(2*g*h)

= sqrt(2*32*100)

= 80 ft/s

b) h = 0.5*g*t^2

t = sqrt(2*h/g)

= sqrt(2*10/32)

= 0.79 s

2)

a)

let v is the velocity of tomato at window

h = v*t + 0.5*g*t^2

450 = v*3 + 0.5*32*3^2

v = 102 ft/s

we know, v = u + a*t

u = v - a*t

= 102 - 32*2

= 38 ft/s <<<<<<<------------Answer

b)
H = h + u*t + 0.5*g*t^2

= 450 + 38*2 + 0.5*32*2^2

= 590 ft <<<<<------Answer

3)

let u is the speed at window.

h = u*t + 0.5*g*t^2

450 = u*2 + 0.5*32*2^2

u = 193 ft/s

let t is the time taken to reach from maximum height to window.

u = g*t

t = u/g

= 193/32

= 6.03 s

total time flight, T = 6.03 + 2 = 8.03 s

now, H = 0.5*g*T^2

= 0.5*32*8.03^2

= 1032 ft

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