Question

A stone is dropped from a height of 10cm above the top of a window 80 cm high. The time taken by
the stone to cross the window is (g = 9.8 ms?)
​

Answer 1

Answer:

0.286 seconds

Explanation:

From the question :-

Height of window = 80 cm

Height of stone from the window = 10 cm

Acceleration due to gravity = 9.8 m/s

To find = time for the stone to cross the window.

Solution :-

Final velocity of stone when it reaches the top of window :-

Initial velocity = 0 m/s (u)

Height = 10 cm or 0.1 m (h)

Acceleration due to gravity = 9.8 m/s (g)

Time = t

Final velocity = v

(By second kinematical equation)

h = g*t + 1/2*g*t²

0.1 = 0*t + 1/2*9.8*t²

0.1 = 0 + 4.9*t²

0.1/4.9 = t²

1/49 = t²

√1/49 = t

1/7 sec. = t

(By first kinematical equation)

v = u + g*t

v = 0 + 9.8*1/7

v = 1.4 m/s

Time taken to cross the window :-

(Now, final velocity of stone when it reaches the top of window is the initial velocity here.

Initial velocity = 1.4 m/s (u)

Height = 80 cm or 0.8 m (h)

Acceleration due to gravity = 9.8 m/s (g)

Final velocity = v

Time = t

(By third kinematical equation)

v² - u² = 2*g*h

v² - 1.4² = 2*9.8*0.8

v² - 1.96 = 15.68

v² = 15.68 + 1.96

v² = 17.64

v = √17.64

v = 4.2 m/s

(By first kinematical equation)

v = u + g*t

4.2 = 1.4 + 9.8*t

4.2 - 1.4 = 9.8*t

2.8 = 9.8*t

2.8/9.8 = t

28/98 = t

0.285714 sec. = t

0.286 sec. = t (rounded off 1/1000)

Hence, the time taken by the stone is 0.286 seconds.