When you go "down" the food chain by continuing to ask "what does it eat?" at what category of living things do you always end u
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Answer:
The equation of simple harmonic motion is
Explanation:
Given that,
Amplitude = 5 inches
Frequency
As per the question initial displacement is zero at t = 0 for sine curve.
The displacement is zero so the phase difference will be zero.
We know that,
The general equation of simple harmonic motion
Where, A = amplitude
= angular frequency
= phase shift
We need to calculate the time period
Using formula of frequency
Put the value into the formula
We need to calculate the angular frequency
Using formula of angular frequency
Put the value into the general equation
Hence, The equation of simple harmonic motion is
<h2>The angle of the initial velocity with respect to the horizontal is 85.14°</h2>
Explanation:
Given that the ball takes 3 seconds to reach its maximum height.
Consider the vertical motion of ball till maximum height.
We have equation of motion v = u + at
Acceleration, a = -9.81 m/s²
Final velocity, v = 0 m/s
Time, t = 3 s
Substituting
v = u + at
0 = u + -9.81 x 3
u = 29.43 m/s
Initial vertical velocity is 29.43 m/s.
Now consider horizontal motion of ball.
Time of flight of ball = 2 x Time to reach maximum height = 2 x 3 = 6 s
Displacement = 15 m
We have equation of motion s = ut + 0.5 at²
Displacement, s = 15 m
Acceleration, a = 0 m/s²
Time, t = 6 s
Substituting
s = ut + 0.5 at²
15 = u x 6 + 0.5 x 0 x 6²
u = 2.5 m/s
Initial horizontal velocity is 2.5 m/s
Let r be the initial velocity and θ be the angle with horizontal
Initial vertical velocity = rsinθ = 29.43 m/s
Initial horizontal velocity = rcosθ = 2.5 m/s
Dividing
The angle of the initial velocity with respect to the horizontal is 85.14°