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The stone projected vertically upwards moves under the action of gravity alone and its motion is described by x = 49 t – 4.9 t2 . It is at a maximum height when
- a)t = 10
- b)t = 5
- c)t = 0
- d)none of these
Correct answer is option 'B'. Can you explain this answer?
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The stone projected vertically upwards moves under the action of gravi...
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The stone projected vertically upwards moves under the action of gravi...
Explanation:
To find the maximum height of the stone, we need to determine the time at which the stone reaches its maximum height.
The equation given for the motion of the stone is x = 49t - 4.9t^2, where x is the height of the stone at time t.
To find the maximum height, we need to find the time at which the velocity of the stone becomes zero. This is because at the maximum height, the stone momentarily comes to rest before it starts falling back down due to gravity.
Step 1: Finding the velocity function
To find the velocity function v(t), we take the derivative of the position function x(t) with respect to time t.
x(t) = 49t - 4.9t^2
v(t) = dx(t)/dt = 49 - 9.8t
Step 2: Setting the velocity function to zero
To find the time at which the velocity becomes zero, we set v(t) = 0 and solve for t.
49 - 9.8t = 0
9.8t = 49
t = 49/9.8
t = 5
So, the time at which the velocity becomes zero is t = 5.
Step 3: Finding the maximum height
To find the maximum height, we substitute the value of t = 5 into the position function x(t).
x(5) = 49(5) - 4.9(5^2)
x(5) = 245 - 122.5
x(5) = 122.5
So, the maximum height of the stone is 122.5 units.
Conclusion:
The stone reaches its maximum height at t = 5. Therefore, the correct answer is option B.
To find the maximum height of the stone, we need to determine the time at which the stone reaches its maximum height.
The equation given for the motion of the stone is x = 49t - 4.9t^2, where x is the height of the stone at time t.
To find the maximum height, we need to find the time at which the velocity of the stone becomes zero. This is because at the maximum height, the stone momentarily comes to rest before it starts falling back down due to gravity.
Step 1: Finding the velocity function
To find the velocity function v(t), we take the derivative of the position function x(t) with respect to time t.
x(t) = 49t - 4.9t^2
v(t) = dx(t)/dt = 49 - 9.8t
Step 2: Setting the velocity function to zero
To find the time at which the velocity becomes zero, we set v(t) = 0 and solve for t.
49 - 9.8t = 0
9.8t = 49
t = 49/9.8
t = 5
So, the time at which the velocity becomes zero is t = 5.
Step 3: Finding the maximum height
To find the maximum height, we substitute the value of t = 5 into the position function x(t).
x(5) = 49(5) - 4.9(5^2)
x(5) = 245 - 122.5
x(5) = 122.5
So, the maximum height of the stone is 122.5 units.
Conclusion:
The stone reaches its maximum height at t = 5. Therefore, the correct answer is option B.
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The stone projected vertically upwards moves under the action of gravity alone and its motion is described by x = 49 t – 4.9t2. It is at a maximum height whena)t = 10b)t = 5c)t = 0d)none of theseCorrect answer is option 'B'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The stone projected vertically upwards moves under the action of gravity alone and its motion is described by x = 49 t – 4.9t2. It is at a maximum height whena)t = 10b)t = 5c)t = 0d)none of theseCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The stone projected vertically upwards moves under the action of gravity alone and its motion is described by x = 49 t – 4.9t2. It is at a maximum height whena)t = 10b)t = 5c)t = 0d)none of theseCorrect answer is option 'B'. Can you explain this answer?.
The stone projected vertically upwards moves under the action of gravity alone and its motion is described by x = 49 t – 4.9t2. It is at a maximum height whena)t = 10b)t = 5c)t = 0d)none of theseCorrect answer is option 'B'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The stone projected vertically upwards moves under the action of gravity alone and its motion is described by x = 49 t – 4.9t2. It is at a maximum height whena)t = 10b)t = 5c)t = 0d)none of theseCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The stone projected vertically upwards moves under the action of gravity alone and its motion is described by x = 49 t – 4.9t2. It is at a maximum height whena)t = 10b)t = 5c)t = 0d)none of theseCorrect answer is option 'B'. Can you explain this answer?.
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