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A balloon is moving up from the ground in such a way that is acceleration is linearly decreasing with its height above the ground. It starts from the ground with acceleration 4m/s2 and with zero initial velocity its acceleration becomes zero at a height 3m. The speed of the balloon at a height 1. 5m/s?
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A balloon is moving up from the ground in such a way that is accelerat...
if a is changing linearly(i.e.gradually with same rate),
=>da/dh=slope of the a vs h graph= (4-0)/(0-3) (as at h=0 =>a=4 and at h=3 =>a=0)
=>da/dh= −4/3
=>da=−(4/3)dh
on intergrating a=−(4/3)h +C
as a=4 => h=0
C=4
therefore,
a=−(4/3)h + 4
=>dv/dt=−(4/3)+4
=>(dv/dh)x(dh/dt)=−(4/3)h + 4 we know dh/dt=v
=>(dv/dh)x(v)=−(4/3)h + 4
=>dvxv={−(4/3)h + 4}dh
on intergrating,
=>v2/2={−(2/3)h2 + 4h + c)
since v=0=>h=0
c=0
=>v2/2=−(2/3)h2 + 4h
when h=1.5
=>v2/2= 4x1.5 − (2/3)x1.52
=>v2/2=6−1.5=4.5
=>v2=9
=>v=3 m/s−1
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A balloon is moving up from the ground in such a way that is accelerat...
Understanding the problem:
We are given that a balloon is moving upwards from the ground, and its acceleration is linearly decreasing with its height above the ground. The balloon starts from the ground with an acceleration of 4 m/s^2 and has zero initial velocity. The acceleration of the balloon becomes zero at a height of 3 m.
We need to determine the speed of the balloon at a height of 1.5 m/s.
Solution:
To find the speed of the balloon at a height of 1.5 m/s, we can use the equations of motion. Let's break down the problem into steps:
Step 1: Determine the time taken to reach a height of 3 m:
We know that the acceleration of the balloon is linearly decreasing with height. Since the acceleration becomes zero at a height of 3 m, we can use the following equation to find the time taken to reach this height:
v = u + at
0 = 0 + 4t
t = 0
Therefore, it takes 0 seconds for the balloon to reach a height of 3 m.
Step 2: Determine the acceleration at a height of 1.5 m:
Since the acceleration is linearly decreasing with height, we can assume that it follows a linear equation of the form:
a = mx + c
where a is the acceleration, x is the height, m is the slope of the line, and c is the y-intercept.
We are given that the acceleration becomes zero at a height of 3 m. Substituting these values into the equation, we get:
0 = m(3) + c
Similarly, at a height of 0 m (starting point), the acceleration is 4 m/s^2. Substituting these values into the equation, we get:
4 = m(0) + c
c = 4
Therefore, the equation for acceleration becomes:
a = mx + 4
To find the value of m, we can use the fact that the acceleration is zero at a height of 3 m:
0 = m(3) + 4
m = -4/3
Therefore, the equation for acceleration becomes:
a = (-4/3)x + 4
Now, we can find the acceleration at a height of 1.5 m by substituting x = 1.5 into the equation:
a = (-4/3)(1.5) + 4
a = -2 + 4
a = 2 m/s^2
Step 3: Determine the speed at a height of 1.5 m:
To find the speed at a height of 1.5 m, we can use the equation of motion:
v^2 = u^2 + 2as
where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the displacement.
Since the initial velocity is zero, the equation simplifies to:
v^2 = 2as
Substituting the values, we get:
v^2 = 2(2)(1.5)
v^2 = 6
v = √6 m/s
Therefore, the speed of the balloon at a height of 1.5 m/s is approximately √6 m/s.
We are given that a balloon is moving upwards from the ground, and its acceleration is linearly decreasing with its height above the ground. The balloon starts from the ground with an acceleration of 4 m/s^2 and has zero initial velocity. The acceleration of the balloon becomes zero at a height of 3 m.
We need to determine the speed of the balloon at a height of 1.5 m/s.
Solution:
To find the speed of the balloon at a height of 1.5 m/s, we can use the equations of motion. Let's break down the problem into steps:
Step 1: Determine the time taken to reach a height of 3 m:
We know that the acceleration of the balloon is linearly decreasing with height. Since the acceleration becomes zero at a height of 3 m, we can use the following equation to find the time taken to reach this height:
v = u + at
0 = 0 + 4t
t = 0
Therefore, it takes 0 seconds for the balloon to reach a height of 3 m.
Step 2: Determine the acceleration at a height of 1.5 m:
Since the acceleration is linearly decreasing with height, we can assume that it follows a linear equation of the form:
a = mx + c
where a is the acceleration, x is the height, m is the slope of the line, and c is the y-intercept.
We are given that the acceleration becomes zero at a height of 3 m. Substituting these values into the equation, we get:
0 = m(3) + c
Similarly, at a height of 0 m (starting point), the acceleration is 4 m/s^2. Substituting these values into the equation, we get:
4 = m(0) + c
c = 4
Therefore, the equation for acceleration becomes:
a = mx + 4
To find the value of m, we can use the fact that the acceleration is zero at a height of 3 m:
0 = m(3) + 4
m = -4/3
Therefore, the equation for acceleration becomes:
a = (-4/3)x + 4
Now, we can find the acceleration at a height of 1.5 m by substituting x = 1.5 into the equation:
a = (-4/3)(1.5) + 4
a = -2 + 4
a = 2 m/s^2
Step 3: Determine the speed at a height of 1.5 m:
To find the speed at a height of 1.5 m, we can use the equation of motion:
v^2 = u^2 + 2as
where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the displacement.
Since the initial velocity is zero, the equation simplifies to:
v^2 = 2as
Substituting the values, we get:
v^2 = 2(2)(1.5)
v^2 = 6
v = √6 m/s
Therefore, the speed of the balloon at a height of 1.5 m/s is approximately √6 m/s.
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A balloon is moving up from the ground in such a way that is acceleration is linearly decreasing with its height above the ground. It starts from the ground with acceleration 4m/s2 and with zero initial velocity its acceleration becomes zero at a height 3m. The speed of the balloon at a height 1. 5m/s?
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A balloon is moving up from the ground in such a way that is acceleration is linearly decreasing with its height above the ground. It starts from the ground with acceleration 4m/s2 and with zero initial velocity its acceleration becomes zero at a height 3m. The speed of the balloon at a height 1. 5m/s? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about A balloon is moving up from the ground in such a way that is acceleration is linearly decreasing with its height above the ground. It starts from the ground with acceleration 4m/s2 and with zero initial velocity its acceleration becomes zero at a height 3m. The speed of the balloon at a height 1. 5m/s? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A balloon is moving up from the ground in such a way that is acceleration is linearly decreasing with its height above the ground. It starts from the ground with acceleration 4m/s2 and with zero initial velocity its acceleration becomes zero at a height 3m. The speed of the balloon at a height 1. 5m/s?.
A balloon is moving up from the ground in such a way that is acceleration is linearly decreasing with its height above the ground. It starts from the ground with acceleration 4m/s2 and with zero initial velocity its acceleration becomes zero at a height 3m. The speed of the balloon at a height 1. 5m/s? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about A balloon is moving up from the ground in such a way that is acceleration is linearly decreasing with its height above the ground. It starts from the ground with acceleration 4m/s2 and with zero initial velocity its acceleration becomes zero at a height 3m. The speed of the balloon at a height 1. 5m/s? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A balloon is moving up from the ground in such a way that is acceleration is linearly decreasing with its height above the ground. It starts from the ground with acceleration 4m/s2 and with zero initial velocity its acceleration becomes zero at a height 3m. The speed of the balloon at a height 1. 5m/s?.
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