Billy and Bob want to know if the amount of baking soda added to vinegar will affect the height a rocket will launch. They will
2 answers:
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The horizontal distance covered by the ball before hitting the water is 70.4 m
Explanation:
The motion of the ball is the motion of a projectile, so it consists of two independent motions:
- A uniform motion along the horizontal (x) direction
- A uniformly accelerated motion along the vertical (y) direction
We start by calculating the time of flight of the ball. This can be done by analyzing the vertical motion. We can use the following suvat equation:
where:
s = -16.5 m is the vertical displacement of the ball (it is negative because we take upward as positive direction)
is the initial vertical velocity of the ball, which is given by
where
u = 23.5 m/s is the initial velocity
is the angle of projection
Substituting,
is the acceleration of gravity, downward
Substituting everything into the equation we get:
Solving the equation for t, we find the time of flight of the ball:
t = -0.94 s
t = 3.59 s
We ignore the 1st solution since it is negative, so the ball reaches the water after 3.59 seconds.
Now we analyze the horizontal motion of the ball. The horizontal velocity is constant and it is:
Therefore, the horizontal distance covered in a time t is
And substituting t = 3.59 s, we find
So, the horizontal distance covered by the ball before hitting the water is 70.4 m.
Learn more about projectile motion:
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<h2>Hello!</h2>
The answer is: 8.62m
<h2>Why?</h2>There are involved two types of mechanical energy: kinetic energy and potential energy, in two different moments.
<h2>First moment:</h2>Before the ball is thrown, where the potential energy is 0.
<h2>Second moment: </h2>After the ball is thrown, at its maximum height, the Kinetic Energy turns to 0 (since at maximum height,the speed is equal to 0) and the PE turns to its max value.
Therefore,
Where:
<em>E</em> is the total energy
<em>PE</em> is the potential energy
<em>KE</em> is the kinetic energy
<em>m</em> is the mass of the object
<em>g</em> is the gravitational acceleration
<em>h </em>is the reached height of the object
<em>v</em> is the velocity of the object
Since the total energy is always constant, according to the Law of Conservation of Energy, we can write the following equation:
Remember, at the first moment the PE is equal to 0 since there is not height, and at the second moment, the KE is equal to 0 since the velocity at maximum height is 0.
So,
Hence,
The height at the second moment (maximum height) is 8.62m
Have a nice day!