Question #e1645
1 Answer
Explanation:
We're asked to find
-
the height of the tower
-
the velocity at which the ball strikes the ground
from the given information.
Height of Tower
This will be the initial position
ul(y = y_0 + v_(0y)t - 1/2g t^2
where
-
y is the final position (ground level,0 ) -
y_0 is the initial position (what we're trying to find) -
v_(0y) is the initial velocity of the ball (given as19.6 "m/s" ) -
t is the time of the motion (given as5 "s" ) -
g = 9.8 "m/s"^2
Plugging in known values:
0 = y_0 + (19.6color(white)(l)"m/s")(5color(white)(l)"s") - 1/2(9.8color(white)(l)"m/s"^2)(5color(white)(l)"s")^2
color(red)(ulbar(|stackrel(" ")(" "y_0 = 24.5color(white)(l)"m"" ")|)
The
Final Velocity
To find the final velcoity, we can use the equation
ul(v_y = v_(0y) - g t
where
-
v_y is the final velocity (what we're trying to find) -
v_(0y) is the initial velocity (19.6 "m/s" ) -
g = 9.81 "m/s"^2 -
t is the time (5 "s" )
Plugging these in:
v_y = 19.6color(white)(l)"m/s" - (9.8color(white)(l)"m/s"^2)(5color(white)(l)"s")
color(blue)(ulbar(|stackrel(" ")(" "v_y = -29.4color(white)(l)"m/s"" ")|)
The final