Answer:
v = 46.99 m/s
Explanation:
The velocity of the ball just before it touches the ground, is given by the following formula:
[tex]v=\sqrt{v_x^2+v_y^2}[/tex] Â Â Â Â Â (1)
vx: horizontal component of the velocity
vy: vertical component of the velocity
The vertical component vy is calculated by using the following formula:
[tex]v_y^2=v_{oy}^2+2gh[/tex] Â (2)
vy: final velocity
voy: initial vertilal velocity = 0m/s  (because it is a semi parabolic motion)
g: gravitational acceleration = 9.8 m/s^2
h: height = 1.60m
You replace the values of the parameters in the equation (2):
[tex]v_y=2(9.8m/s^2)(1.60m)=31.36\frac{m}{s}[/tex]
vx is calculated by using the information about the horizontal range of the ball:
[tex]R=v_o\sqrt{\frac{2h}{g}}[/tex] Â Â (3)
R: horizontal range of the ball = 20.0 m
You solve the previous equation for vo, the initial horizontal velocity:
[tex]v_o=R\sqrt{\frac{g}{2h}}=(20.0m)\sqrt{\frac{9.8m/s^2}{2(1.60m)}}\\\\v_o=35\frac{m}{s}[/tex]
The horizontal component of the velocity is constant in the complete trajectory, hence, you have that
vx = vo = 35 m/s
Finally, you replace the values of vx and vy in the equation (1):
[tex]v=\sqrt{(35m/s)^2+(31.36m/s)^2}=46.99\frac{m}{s}[/tex]
The velocity of the ball just before it touches the ground is 46.99 m/s
