1. Suppose you look out the window of a skyscraper and see someone throw a tomat

Question

1. 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.

(a) Find the velocity (with the positive direction pointing up) at which the tomato was thrown.  

(b) Find the height from which the tomato was thrown.

2.(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

Equation 1 --

(H - 450) = VT + (1/2)(g)T^2

H = height above window where the tomato was thrown
V = initial velocity at which tomato was thrown
g = acceleration due to gravity = 32.2 ft/sec^2 (constant)

Substituting values,

H = V(2) + (1/2)(32.2)(2^2)

H = 2V + 64.4

Equation 2 --

H + 450 = VT + (1/2)gT^2

and substituting appropriate values,

H = V(5) + (1/2)(32.2)(5^2) - 450

H = 5V + 402.5 - 450

H = 5V - 47.5

Since Equation 1 = Equation 2

2V + 64.4 = 5V - 47.5

3V = 111.9

V = 37.3 ft/sec.

NOTE -- this is close enough to the book answer of 38 fps. The book has a negative sign just as a matter of convention. It designated the speed of direction going downward as negative while my solution assumed positive signs for the downward velocity.

Going back to Equation 1 to solve for "H"

H = 2(37.3) + 64.4

H = 139 feet

Therefore, height of the building would be

139 + 450 = 589 feet.

NOTE -- again, this is close enough to the book answer of 590 ft.

Take 450 from your window to ground and divide it by 2 to find average velocity it takes to hit the ground.
450ft/2sec= 225 ft/sec
then subtract 32ft/sec because it takes 2 seconds so it is going to be going 32ft/sec slower when its at your window. 225ft/sec -32 ft/sec =193 ft/sec
Then you can use V=at equation. So 193ft/sec /(32ft/sec^2) = 6.03125 sec
You can use that time to plug into D=1/2at^2
D=1/2*32ft/sec^2(6.03125sec)^2=582ft
Then add original 450 ft. 582ft+450ft=1032ft

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