
If a body travels half its total path in the last second of its fall from rest. The time and height of its fall are,
(A)
(B)
(C)
(D)
Answer
139.5k+ views
Hint: We solve this question by using the second equation of motion to find the time of free fall. We first get an equation for distance travelled by body in time . We then find an equation for distance travelled by body in time . Subtracting both equations, we get the time of free fall as well as the distance of free fall.
Formula used: second equation of motion is equal to
Here, Distance is represented by
Initial velocity is represented by
Time is represented by
Acceleration is represented by
Complete step by step answer:
Since the body is falling freely the initial velocity will be zero
The second equation of motion for free fall is equal to
Finding the distance travelled by the body in time
Let us consider the distance travelled by body in time as
.......(1)
Here, we take acceleration as acceleration due to gravity which is represented by because in a free fall the body is accelerated only due to gravity.
Now finding the distance travelled by body in time
Let us consider the distance travelled by body in time as
........(2)
Subtracting (2) from (1) we get the distance travelled in the last one second.
From the question the distance travelled by body in the last one second is equal to
Substituting this in the above equation we get
......(3)
From equation (1)
Equation (3) now becomes
Solving for t we get
Solving the polynomial equation, we get,
From the question the body travels only half the distance in the last one second this means that the total time must be greater than one sec. Thus, time of free fall is equal to
We height if free fall is nothing but the total distance travelled by the body. From equation (1)
Substituting the value of
Hence option (A) is the correct answer.
Note: It is to be remembered that in a free fall of a body the initial velocity is always zero unless the question mentions something else. Also, the only acceleration acting on the body will be the acceleration due to gravity unless the question mentions any additional information. One must remember these points to not make a mistake.
Formula used: second equation of motion is equal to
Here, Distance is represented by
Initial velocity is represented by
Time is represented by
Acceleration is represented by
Complete step by step answer:
Since the body is falling freely the initial velocity will be zero
The second equation of motion for free fall is equal to
Finding the distance travelled by the body in time
Let us consider the distance travelled by body in time
Here, we take acceleration as acceleration due to gravity which is represented by
Now finding the distance travelled by body in time
Let us consider the distance travelled by body in time
Subtracting (2) from (1) we get the distance travelled in the last one second.
From the question the distance travelled by body in the last one second is equal to
Substituting this in the above equation we get
From equation (1)
Equation (3) now becomes
Solving for t we get
Solving the polynomial equation, we get,
From the question the body travels only half the distance in the last one second this means that the total time must be greater than one sec. Thus, time of free fall is equal to
We height if free fall is nothing but the total distance travelled by the body. From equation (1)
Substituting the value of
Hence option (A)
Note: It is to be remembered that in a free fall of a body the initial velocity is always zero unless the question mentions something else. Also, the only acceleration acting on the body will be the acceleration due to gravity unless the question mentions any additional information. One must remember these points to not make a mistake.
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