A tennis ball is thrown from ground level with velocity directed 30° above the horizontal. if it takes the ball 0.5 s to reach t
1 answer:
The motion of the tennis ball on the vertical axis is an uniformly accelerated motion, with deceleration of 
(gravitational acceleration).
The component of the velocity on the y-axis is given by the following law:
At the time t=0.5 s, the ball reaches its maximum height, and when this happens, the vertical velocity is zero (because it is a parabolic motion):
. Substituing into the previous equation, we find the initial value of the vertical component of the velocity:
However, this is not the final answer. In fact, the ball starts its trajectory with an angle of
. This means that the vertical component of the initial velocity is
We found before
, so we can substitute to find 
, the initial speed of the ball:
The component of the velocity on the y-axis is given by the following law:
At the time t=0.5 s, the ball reaches its maximum height, and when this happens, the vertical velocity is zero (because it is a parabolic motion):
However, this is not the final answer. In fact, the ball starts its trajectory with an angle of
We found before
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a. The free-body diagram for the glass when it is at the top of the circle is attached below.
b. The equation for the net force on the glass at the top of the circle in terms of w, Fn, m, v, and r is mg x g + N - mg x Vtop² /R =0
c. The glass will fall out of the bucket if the normal force between the glass and bucket equals zero. The speed with which she spin the bucket to prevent this from happening is 3.83 m/s.
d. The string will break if the tension on it is more than 100 N. The range of speeds can prevent the string from breaking is 3.83< Vtop<4.99 m/s
<h3>What is Net force?</h3>When two or more forces are acting on the system of objects, then the to attain equilibrium, net force must be zero.
Given, Angela has a bucket of mass 2 kg tied to a string. She places a drinking glass of mass 0.5 kg in the bucket. She spins the bucket in a vertical circle of radius 1.5 m. She must swing the bucket to keep the glass from falling out.
a. The free body diagram of the bucket and glass is attached below.
b. Bucket will undergo centrifugal force
Fb = mVtop² /R
From the equilibrium of forces, we have
For bucket,
T +mb xg - N = mb x Vtop² /R..............(1)
For glass,
mg x g + N = mg x Vtop² /R..............(2)
Thus, this is the net force equation on the glass.
c. On adding both the equations. we have
T + (mb + mg) xg = (mb + mg) Vtop² /R
Substituting the values, T = 0 and from the question, we get
0 + (2+0.5) 9.81 = (2+0.5)(Vtop²/0.5)
Vtop = 3.83 m/s
Thus, the speed of spin to prevent glass from falling out is 3.83 m/s
d. The string will break if the tension on it is more than 100 N
100 + (2+0.5) 9.81 = (2+0.5)(Vtop²/0.5)
Vtop = 4.99 m/s
Thus, the range of velocity is 3.83< Vtop<4.99 m/s
Learn more about net force.
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