A ball is thrown vertically downward from the top of a 35.9-m tall building. The ball then passes the top of a window that is 10.7 m above the ground 2.00 s after being thrown.
What is the speed of the ball as it passes the top of the window?
The equation for the speed of the ball, from time t=0 when the ball is released, is
V = Vo + g t
Vo it the initial velocity of the ball. The distance it has travelled at time t, measured vertically downward, is
Y = Vo t + (1/2) g t^2
You know that Y = 25.2 m at t = 2.
Use that information and the last equation to determine Vo. Then use that Vo in the first equation to get the value of V when t = 2.
25.2=Vo(2)+.5(-9.8)(2^2)
25.2=Vo(2)-19.6
25.2+19.6=2Vo
45.1=2Vo
Vo=22.55m/s
V=Vo + gt
V= 22.55 +9.8*2
V= 42.15 m/s
Displacement should be in negative... as the ball thrown vertically downward.....
So we solve.... s=ut - 1/2gt^2..... put t=2, s=-25.2m
After obtaining the value of u...using 1st eqn of motion... v=u-gt
Then v is ur required answer
To find the speed of the ball as it passes the top of the window, we can follow the steps given. First, we need to determine the initial velocity (Vo) of the ball.
Given:
- The ball is thrown vertically downward from the top of a 35.9 m tall building.
- The ball passes the top of a window that is 10.7 m above the ground 2.00 s after being thrown.
- The distance travelled at time t is given by Y = Vo t + (1/2) g t^2.
- At t = 2, Y = 25.2 m.
Step 1: Determine the value of Vo using the equation Y = Vo t + (1/2) g t^2.
Substitute the given values into the equation: 25.2 m = Vo * 2 + (1/2) * (-9.8 m/s^2) * (2 s)^2.
Simplifying the equation:
25.2 m = 2Vo - 19.6 m/s^2.
2Vo = 25.2 m + 19.6 m/s^2.
2Vo = 44.8 m.
Vo = 44.8 m / 2.
Vo = 22.4 m/s.
Step 2: Use the value of Vo in the equation V = Vo + g t to find V at t = 2.
Substitute the values into the equation: V = 22.4 m/s + (-9.8 m/s^2) * 2 s.
Simplifying the equation:
V = 22.4 m/s + (-19.6 m/s).
V = 22.4 m/s - 19.6 m/s.
V = 2.8 m/s.
Therefore, the speed of the ball as it passes the top of the window is 2.8 m/s.