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A body is thrown vertically upwards with a speed of 10 m/s from a tower of height 26.25 m. The magnitude of the average vel for the whole journey is (1) 17.5 m/s (2) 3 m/s (3) 25 m/s (4) 7.5 m/s?
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A body is thrown vertically upwards with a speed of 10 m/s from a towe...
Given:
Initial velocity (u) = 10 m/s (upwards)
Height (h) = 26.25 m
To find:
Magnitude of the average velocity for the whole journey
Solution:
Step 1: Finding the time taken to reach the maximum height (t1)
Using the equation of motion:
v = u - gt
Where,
v = final velocity (0 m/s at the maximum height)
g = acceleration due to gravity (-9.8 m/s²)
u = initial velocity (10 m/s)
0 = 10 - 9.8t1
9.8t1 = 10
t1 = 10/9.8
t1 ≈ 1.02 s
Step 2: Finding the time taken to fall from the maximum height (t2)
Using the equation of motion:
h = ut - (1/2)gt²
Where,
h = height (26.25 m)
u = initial velocity (0 m/s at the maximum height)
g = acceleration due to gravity (-9.8 m/s²)
26.25 = 0 × t2 - (1/2) × (-9.8) × t2²
26.25 = (4.9/2) × t2²
t2² = (2 × 26.25) / 4.9
t2² = 13.5 / 4.9
t2² ≈ 2.76
t2 ≈ √2.76
t2 ≈ 1.66 s
Step 3: Finding the total time of the journey (t)
Since the body goes up and then comes back down, the total time is given by:
t = t1 + t2
t = 1.02 + 1.66
t ≈ 2.68 s
Step 4: Finding the average velocity for the whole journey (v_avg)
Using the equation:
v_avg = total displacement / total time
The total displacement is the height of the tower (26.25 m). Therefore:
v_avg = 26.25 / 2.68
v_avg ≈ 9.78 m/s
Therefore, the magnitude of the average velocity for the whole journey is approximately 9.78 m/s.
Answer:
The magnitude of the average velocity for the whole journey is 9.78 m/s.
Initial velocity (u) = 10 m/s (upwards)
Height (h) = 26.25 m
To find:
Magnitude of the average velocity for the whole journey
Solution:
Step 1: Finding the time taken to reach the maximum height (t1)
Using the equation of motion:
v = u - gt
Where,
v = final velocity (0 m/s at the maximum height)
g = acceleration due to gravity (-9.8 m/s²)
u = initial velocity (10 m/s)
0 = 10 - 9.8t1
9.8t1 = 10
t1 = 10/9.8
t1 ≈ 1.02 s
Step 2: Finding the time taken to fall from the maximum height (t2)
Using the equation of motion:
h = ut - (1/2)gt²
Where,
h = height (26.25 m)
u = initial velocity (0 m/s at the maximum height)
g = acceleration due to gravity (-9.8 m/s²)
26.25 = 0 × t2 - (1/2) × (-9.8) × t2²
26.25 = (4.9/2) × t2²
t2² = (2 × 26.25) / 4.9
t2² = 13.5 / 4.9
t2² ≈ 2.76
t2 ≈ √2.76
t2 ≈ 1.66 s
Step 3: Finding the total time of the journey (t)
Since the body goes up and then comes back down, the total time is given by:
t = t1 + t2
t = 1.02 + 1.66
t ≈ 2.68 s
Step 4: Finding the average velocity for the whole journey (v_avg)
Using the equation:
v_avg = total displacement / total time
The total displacement is the height of the tower (26.25 m). Therefore:
v_avg = 26.25 / 2.68
v_avg ≈ 9.78 m/s
Therefore, the magnitude of the average velocity for the whole journey is approximately 9.78 m/s.
Answer:
The magnitude of the average velocity for the whole journey is 9.78 m/s.
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A body is thrown vertically upwards with a speed of 10 m/s from a tower of height 26.25 m. The magnitude of the average vel for the whole journey is (1) 17.5 m/s (2) 3 m/s (3) 25 m/s (4) 7.5 m/s?
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A body is thrown vertically upwards with a speed of 10 m/s from a tower of height 26.25 m. The magnitude of the average vel for the whole journey is (1) 17.5 m/s (2) 3 m/s (3) 25 m/s (4) 7.5 m/s? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A body is thrown vertically upwards with a speed of 10 m/s from a tower of height 26.25 m. The magnitude of the average vel for the whole journey is (1) 17.5 m/s (2) 3 m/s (3) 25 m/s (4) 7.5 m/s? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A body is thrown vertically upwards with a speed of 10 m/s from a tower of height 26.25 m. The magnitude of the average vel for the whole journey is (1) 17.5 m/s (2) 3 m/s (3) 25 m/s (4) 7.5 m/s?.
A body is thrown vertically upwards with a speed of 10 m/s from a tower of height 26.25 m. The magnitude of the average vel for the whole journey is (1) 17.5 m/s (2) 3 m/s (3) 25 m/s (4) 7.5 m/s? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A body is thrown vertically upwards with a speed of 10 m/s from a tower of height 26.25 m. The magnitude of the average vel for the whole journey is (1) 17.5 m/s (2) 3 m/s (3) 25 m/s (4) 7.5 m/s? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A body is thrown vertically upwards with a speed of 10 m/s from a tower of height 26.25 m. The magnitude of the average vel for the whole journey is (1) 17.5 m/s (2) 3 m/s (3) 25 m/s (4) 7.5 m/s?.
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