Answer:
3.1 m/s
Explanation:
First, find the time it takes for the cat to land. Take down to be positive.
Given:
Δy = 0.61 m
v₀ = 0 m/s
a = 9.81 m/s²
Find: t
Δy = v₀ t + ½ at²
(0.61 m) = (0 m/s) t + ½ (9.81 m/s²) t²
t = 0.353 s
Now find the horizontal velocity needed to travel 1.1 m in that time.
Given:
Δx = 1.1 m
a = 0 m/s²
t = 0.353 s
Find: v₀
Δx = v₀ t + ½ at²
(1.1 m) = v₀ (0.353 s) + ½ (0 m/s²) (0.353 s)²
v₀ = 3.1 m/s
Answer:
A skater glides along a circular path. She defines a certain point on the circle as her origin. Later on, she passes through a point at which the distance she has traveled along the path from the origin is smaller than the magnitude of her displacement vector from the origin.
So here in circular motion of the skater we can see that the total path length of the skater is along the arc of the circle while we can say that displacement is defined as the shortest distance between initial and final position of the object.
So it is not possible in any circle that arc-length is less than the chord joining the two points on the circle
As we know that arc length is given as
length of chord is given as
so here
so we have
Answer:
Length of pipe meter
Explanation:
Speed of a transverse wave on a string
where F is the tension in string and is the mass per unit length
Thus,
Substituting the given values we get -
Speed of a transverse wave on a string
For third harmonic wave , frequency is equal to
Substituting the given values, we get -
Length of pipe
Substituting the given values we get
for first harmonic wave
Length of pipe meter
Answer:
K_{total} = 19.4 J
Explanation:
The total kinetic energy that is formed by the linear part and the rotational part is requested
let's look for each energy
linear
= ½ m v²
rotation
= ½ I w²
the moment of inertia of a solid sphere is
I = 2/5 m r²
we substitute
= ½ mv² + ½ I w²
angular and linear velocity are related
v = w r
we substitute
K_{total} = ½ m w² r² + ½ (2/5 m r²) w²
K_{total} = m w² r² (½ + 1/5)
K_{total} = m w² r²
let's calculate
K_{total} = 6.40 16.0² 0.130²
K_{total} = 19.4 J