Answer :
The motion of the tennis ball on the vertical axis is an uniformly accelerated motion, with deceleration of [tex]g=-9.81 m/s^2[/tex] (gravitational acceleration).
The component of the velocity on the y-axis is given by the following law:
[tex]v_y(t) = v_{y0}+gt[/tex]
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): [tex]v_y(0.5 s)=0[/tex]. Substituing into the previous equation, we find the initial value of the vertical component of the velocity:
[tex]v_{y0}=-gt=-(-9.81 m/s^2)(0.5 s)=4.9 m/s[/tex]
However, this is not the final answer. In fact, the ball starts its trajectory with an angle of [tex]30^{\circ}[/tex]. This means that the vertical component of the initial velocity is
[tex]v_{y0}=v_0 sin 30^{\circ}[/tex]
We found before [tex]v_{0y}=4.9 m/s[/tex], so we can substitute to find [tex]v_0[/tex], the initial speed of the ball:
[tex]v_0 = \frac{v_{y0}}{sin 30^{\circ}}=9.81 m/s [/tex]
The component of the velocity on the y-axis is given by the following law:
[tex]v_y(t) = v_{y0}+gt[/tex]
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): [tex]v_y(0.5 s)=0[/tex]. Substituing into the previous equation, we find the initial value of the vertical component of the velocity:
[tex]v_{y0}=-gt=-(-9.81 m/s^2)(0.5 s)=4.9 m/s[/tex]
However, this is not the final answer. In fact, the ball starts its trajectory with an angle of [tex]30^{\circ}[/tex]. This means that the vertical component of the initial velocity is
[tex]v_{y0}=v_0 sin 30^{\circ}[/tex]
We found before [tex]v_{0y}=4.9 m/s[/tex], so we can substitute to find [tex]v_0[/tex], the initial speed of the ball:
[tex]v_0 = \frac{v_{y0}}{sin 30^{\circ}}=9.81 m/s [/tex]