Answer:
a)![t_{1}=3.49s](https://tex.z-dn.net/?f=t_%7B1%7D%3D3.49s)
b)![t_{2}=2.00s](https://tex.z-dn.net/?f=t_%7B2%7D%3D2.00s)
c)Xmax=80.71m
Explanation:
<u>a)Kinematics equation for the Stone, dropped:</u>
![v(t)=v_{o}-g*t](https://tex.z-dn.net/?f=v%28t%29%3Dv_%7Bo%7D-g%2At)
![y(t)=y_{o}+v_{o}t-1/2*g*t^{2}](https://tex.z-dn.net/?f=y%28t%29%3Dy_%7Bo%7D%2Bv_%7Bo%7Dt-1%2F2%2Ag%2At%5E%7B2%7D)
initial position is bridge height
the stone is dropped
The ball reaches the ground, y=0, at t=t1:
![0=h-1/2*g*t_{1}^{2}](https://tex.z-dn.net/?f=0%3Dh-1%2F2%2Ag%2At_%7B1%7D%5E%7B2%7D)
![t_{1}=\sqrt{2h/g}=\sqrt{2*60/9.83}=3.49s](https://tex.z-dn.net/?f=t_%7B1%7D%3D%5Csqrt%7B2h%2Fg%7D%3D%5Csqrt%7B2%2A60%2F9.83%7D%3D3.49s)
<u>b)Kinematics equation for the Stone, with a initial speed of 20m/s:</u>
![v(t)=v_{o}-g*t](https://tex.z-dn.net/?f=v%28t%29%3Dv_%7Bo%7D-g%2At)
![y(t)=y_{o}+v_{o}t-1/2*g*t^{2}](https://tex.z-dn.net/?f=y%28t%29%3Dy_%7Bo%7D%2Bv_%7Bo%7Dt-1%2F2%2Ag%2At%5E%7B2%7D)
initial position is bridge height
the stone is thrown straight down
The ball reaches the ground, y=0, at t=t1:
![0=h+v_{o}t_{2}-1/2*g*t_{2}^{2}](https://tex.z-dn.net/?f=0%3Dh%2Bv_%7Bo%7Dt_%7B2%7D-1%2F2%2Ag%2At_%7B2%7D%5E%7B2%7D)
![0=60-20t_{2}-1/2*9.83*t_{2}^{2}](https://tex.z-dn.net/?f=0%3D60-20t_%7B2%7D-1%2F2%2A9.83%2At_%7B2%7D%5E%7B2%7D)
t2=-6.01 this solution does not have physical sense
t2=2.00
<u>c)Kinematics equation for the Stone, with a initial speed of 20m/s with an angle of 30° above the horizontal:</u>
![v(t)=v_{o}-g*t](https://tex.z-dn.net/?f=v%28t%29%3Dv_%7Bo%7D-g%2At)
![y(t)=y_{o}+v_{o}t-1/2*g*t^{2}](https://tex.z-dn.net/?f=y%28t%29%3Dy_%7Bo%7D%2Bv_%7Bo%7Dt-1%2F2%2Ag%2At%5E%7B2%7D)
initial position is bridge height
the stone is thrown with an angle of 30° above the horizontal
The ball reaches the ground, y=0, at t=t3:
![0=h+v_{o}t_{3}-1/2*g*t_{3}^{2}](https://tex.z-dn.net/?f=0%3Dh%2Bv_%7Bo%7Dt_%7B3%7D-1%2F2%2Ag%2At_%7B3%7D%5E%7B2%7D)
![0=60+10t_{3}-1/2*9.83*t_{3}^{2}](https://tex.z-dn.net/?f=0%3D60%2B10t_%7B3%7D-1%2F2%2A9.83%2At_%7B3%7D%5E%7B2%7D)
t3=-2.62 this solution does not have physical sense
t3=4.66
the movement in x:
v=constant=20cos(30)m/s
x(t)=v*t
Xmax=v*t3=20cos(30)*4.66=80.71m