A projectile is shot from the ground at a velocity of 84 m/s and at an angle of (7pi)/12. How long will it take for the projectile to land?
1 Answer
Aug 5, 2017
Explanation:
We're asked to find the time it takes for a projectile to land, given its initial velocity.
To do this, we can use the kinematics equation
ul(Deltay = v_0sinalpha_0t - 1/2g t^2
where
-
Deltay is the change in height (which is0 when it lands) -
v_0 is the initial speed (given as84 "m/s" ) -
alpha_0 is the launch angle (given as(7pi)/12 ) -
t is the time (what we're trying to find) -
g = 9.81color(white)(l)"m/s"^2
Plugging in known values, we have
0 = (84color(white)(l)"m/s")sin((7pi)/12)t - 1/2(9.81color(white)(l)"m/s"^2)t^2
(4.905color(white)(l)"m/s"^2)t^2 = (81.1color(white)(l)"m/s")t
(4.905color(white)(l)"m/s"^2)t = 81.1color(white)(l)"m/s"
t = color(red)(ulbar(|stackrel(" ")(" "16.5color(white)(l)"s"" ")|)