A student drops an object out the window of the top floor of a high-rise dormito

Question

A student drops an object out the window of the top floor of a high-rise dormitory. (a) Neglecting air resistance, how fast is the object traveling when it strikes the ground at the end of 1.5 s? First used standard British units and then express the speed in mi/h for a familiar comparison. ft/s mi/h Can things dropped from high places be dangerous to people below? Yes No (b) How far, in meters, does the object fall during the 1.5 s? Comment on how many floors the dormitory probably has. (Assume that there are 32 floors/100 m.) m floors

Explanation / Answer

(a)Let v be its speed at time, t = 1.5 sec.

We know from the equation of motion that,

v = u + at

In our case, u = 0 ; a = g = 9.8 m/s2 and t = 1.5 s

v = 0 + (9.8 m/s2) x 1.5 s = 14.7 m/s

Hence, v = 14.7 m/s = 32.9 mi/hr = 48.23 ft/sec.

Yes, things dropped from high places are dangerous to the peole on the ground.

(b)From third equation of motion we know that,

S = ut + 1/2 a t2

In our case,

S = ? ; u = 0 ; a = 9.8 m/s2 ; t = 1.5 sec

S = 0 + 0.5 x 9.8 m/s2 x 1.52 s = 11.03 m

The object fell, S = 11.03 m in 1.5 sec.

Let n b the no of floors. If there are 32floors/100 m then,

0.32 floor per meter, So,

n = 0.32 x 11.03 = 3.53 floors

n has to be an integer so, rounding off to 3.

Hence, number of floors = n = 3.

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