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Question: A ball is dropped from the top of a building. The ball takes 0.5 s to fall past the 3 m length of a ...

A ball is dropped from the top of a building. The ball takes 0.5 s to fall past the 3 m length of a window at certain distances from the top of the building. Time of travel above the window is (Takeg=10m/s2g = 10m/{s^2})
A. 0.5 s
B. 0.25 s
C. 0.35 s
D. 0.75 s

Explanation

Solution

If a body moving in a straight line covers an equal amount of distance in an equal time interval, then the body is said to be uniform motion. The line is represented by the formula x=x0+vtx = {x_0} + vt, where x0{x_0} is the position of the body at the time t=0t = 0.
In this question first, find out the velocity of the body when it falls past the 3 meters windows for the given time and since the body is in uniform motion use this velocity to calculate the time for the body to reach the top of the window from the top of the building.

Complete step by step answer:
Height of window=3m = 3m
Time is taken=0.5s = 0.5s

Hence by using the distance formula calculate the velocity of the ball to travel B to C,

Sy=uyt+12gt2 3=uy×0.5+0.5×10×(0.5)2 3=u×0.5+5×0.25 u×0.5=31.25 u=1.750.5 u=3.5m/s  {S_y} = {u_y}t + \dfrac{1}{2}g{t^2} \\\ \Rightarrow 3 = {u_y} \times 0.5 + 0.5 \times 10 \times {\left( {0.5} \right)^2} \\\ \Rightarrow 3 = u \times 0.5 + 5 \times 0.25 \\\ \Rightarrow u \times 0.5 = 3 - 1.25 \\\ \Rightarrow u = \dfrac{{1.75}}{{0.5}} \\\ \Rightarrow u = 3.5m/s \\\

Now the velocity u=3.5m/su = 3.5m/sbecomes the final velocity when the ball reaches to the top of the window at B from top of building A,
u=v=3.5m/su = v = 3.5m/s
Hence by using the final velocity formula, where initial velocityu=0u = 0, since the ball was at rest at the top of building A,

v=u+gt 3.5=0+10t t=3.510 =0.35sec  v = u + gt \\\ \Rightarrow 3.5 = 0 + 10t \\\ \Rightarrow t = \dfrac{{3.5}}{{10}} \\\ = 0.35\sec \\\

So the time is taken by the ball to reach the top of the window B =0.35sec= 0.35\sec

So, the correct answer is “Option C”.

Note:
Motion with constant velocity is one of the simplest forms of motion. These types of motion occur when the object is moving with the presence of negligible friction. Constant velocity is the motion of a body, moving in a straight line with zero acceleration at a constant speed.