9. The maximum horizontal range of a projectile is given by the formula R= u2/g where u is the initial velocity and g is the acceleration due to gravity. Find the velocity with which a ball can be thrown to have a maximum range of 20 meters when the acceleration due to gravity is equal to 9.8 m/s.(SHOW WORK)

Hello!The answer is:The velocity with which the ball can be thrown to have a maximum range of 20 meters is equal to 14 m/s.[tex]u=14\frac{m}{s}[/tex]Why?To solve the problem and find the velocity, we need to isolate it from the equation used to calculate the maximum horizontal range.We have the equation:[tex]R=\frac{u^{2} }{g}[/tex]Where,R is the maximum horizontal range.u is the initial velocity.g is the gravity acceleration.Also, from the statement we know that:[tex]R=20m\\g=9.8\frac{m}{s^{2} }[/tex]So, using the given information, and isolating, we have:[tex]R=\frac{u^{2} }{g}[/tex][tex]R*g=u^{2}[/tex][tex]u^{2}=R*g=20m*9.8\frac{m}{s^{2} }=196\frac{m^{2} }{s^{2} }\\\\u=\sqrt{196\frac{m^{2} }{s^{2}}}=14\frac{m}{s}[/tex]Hence, we have that the velocity with which the ball can be thrown to have a maximum range of 20 meters is equal to 14 m/s.[tex]u=14\frac{m}{s}[/tex]Have a nice day!