Question

an object falls a distance D from rest . the object travels a distance 0.51D in last 2 seconds. the time taken by the object to cover the distance D is
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Answer 1

Explanation:

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Answer 2

Answer:

The time taken by the object to travel a distance D = $2.8sec$.

Explanation:

Data given,

The total distance = D

The time taken by the object to travel a distance $0.51D$ = $2sec$

The time taken by the object to travel a distance D =?

From the equation of motions, we can find out the time taken to travel a distance D:

For distance $0.51D$;

• S = $ut + \frac{1}{2}at^{2}$

Here, S = distance = $0.51D$

• u = initial velocity = 0 ( starts from rest )
• a = acceleration due to gravity = $9.81m/s^{2}$
• t = time = $2sec$

Therefore,

• S = $\frac{1}{2}\times 9.81 (2)^{2}$
• $0.51D$ = $19.62$
• D = $38.47m$

Now, for total distance D;

• S = $ut + \frac{1}{2}at^{2}$

Here, S = distance = $38.47m$

• u = initial velocity = 0 ( starts from rest )
• a = acceleration due to gravity = $9.81m/s^{2}$

Therefore,

• S = $ut + \frac{1}{2}at^{2}$
• $38.47$ = $\frac{1}{2}\times 9.81t^{2}$
• $t^{2} = 7.84$
• t = $2.8sec$

Hence, the time taken by the object to travel a distance D = $2.8sec$.