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2 answers:
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Explanation:
The linear analog of angle is angle itself.
The linear analog of angular velocity is linear velocity.
ω is angular velocity, therefore linear velocity is given by v
∴ for linear velocity,
for angular velocity,
The linear analog of angular acceleration is acceleration.
α is angular acceleration whereas as a is linear acceleration.
∴ for linear acceleration, v = u + a.t
for angular acceleration,
The linear analog of moment of inertia is mass.
I is moment of inertia and m is mass,
∴ for linear analog, F = m.a
for angular analog, τ - I.α
Answer:
The maximum height reached is 4.63 m.
Explanation:
Given:
Initial speed of the man (u) = 31.0 m/s
Speed at the top of trajectory () = 29.5 m/s
Acceleration due to gravity (g) = 9.8 m/s²
When the man reaches the top of the trajectory, the vertical component of velocity becomes zero and hence only horizontal component of velocity acts on him.
Also, since there is no net force acting in the horizontal direction, the acceleration is zero in the horizontal direction from Newton's second law. Thus, the horizontal component of velocity always remains the same.
So, speed at the top of trajectory is nothing but the horizontal component of initial velocity.
Now, initial velocity can be rewritten in terms of its components as:
Where, are the initial horizontal and vertical velocities of the man.
Now, plug in the given values and simplify. This gives,
Now, we know that, for a projectile motion, the maximum height is given as:
Plug in the value from equation (1) and 9.8 for 'g' to solve for 'H'. This gives,
Therefore, the maximum height reached is 4.63 m.