Question #e1645

1 Answer
Aug 26, 2017

"height" = 24.5 "m"

"velocity" = -29.4 "m/s"

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 y_0 of the ball, and we're going to use the kinematics equation

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 as 19.6 "m/s")

  • t is the time of the motion (given as 5 "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 color(red)("height" of the tower is thus color(red)(24.5color(white)(l)"meters".

" "

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 color(blue)("velocity" of the ball is therefore color(blue)(29.4color(white)(l)"meters per second" in the color(blue)("downward direction".