A projectile is shot from the ground at a velocity of #4 m/s# and at an angle of #(5pi)/6#. How long will it take for the projectile to land?
1 Answer
Explanation:
We're asked to find the time
We can use the equation
to find the time
where

#Deltay# is the change in#y# position (height) of the object, in#"m"# 
#v_(0y)# is the initial#y# velocity of the object, in#"m"/"s"# 
#t# is the time, in#"s"# , and 
#g# is the acceleration due to gravity near Earth's surface,#9.80"m"/("s"^2)# .
To find the initial
where

#v_0# is the magnitude of the initial velocity, in#"m"/"s"# , and 
#alpha# is the initial launch angle.
Plugging in our known variables, we have
Now that we have our known variables necessary, let's plug them back into the original equation to find the times when the height is
We'll eliminate the
rounded to one significant figure, which is the amount given in the problem.
Thus, the object will land again ad