A baseball is thrown such that it is in the air for 4 seconds and lands 100 m away. Find the initial vertical and horizontal components of the baseball's velocity.
Draw the picture and it will make sense.
To find the initial vertical and horizontal components of the baseball's velocity, we can use the equations of motion and the given information.
Given:
Time of flight, t = 4 seconds
Horizontal displacement, x = 100 m
We can first find the initial vertical component of velocity, denoted as Vyi. Since there is no vertical displacement (the baseball goes up and then comes down to the same height), we know that the total time taken to reach the peak of its trajectory is half of the total flight time.
So, the time taken to reach the peak is t/2 = 4/2 = 2 seconds.
Using the equation of motion for vertical displacement, we have:
y = Vyi * t - (1/2) * g * t^2
Since the vertical displacement is zero when the ball is at its highest point, y = 0. Plugging in the values, we get:
0 = Vyi * 2 - (1/2) * g * (2^2)
0 = 2Vyi - 2g
Rearranging the equation, we have:
2Vyi = 2g
Vyi = g
Therefore, the initial vertical component of velocity is equal to the acceleration due to gravity, which is approximately 9.8 m/s^2.
Next, we can find the initial horizontal component of velocity, denoted as Vxi. We know that the horizontal displacement, x = Vxi * t.
Plugging in the values, we get:
100 = Vxi * 4
Vxi = 100/4
Vxi = 25 m/s
Therefore, the initial horizontal component of velocity is 25 m/s.
To summarize:
- Initial vertical component of velocity (Vyi) = g (approximately 9.8 m/s^2)
- Initial horizontal component of velocity (Vxi) = 25 m/s