Upton Chuck is riding the Giant Drop at Great America. If Upton free falls for 2.6 seconds, what will be his final velocity and how far will he fall?
Don't forget to divide the 1/2 out of the equation. 9.8 will become 4.9 a lot of people make the mistake of forgetting to cancel and divide 1/2.
a. V = Vo + gt
V = 0 + 9.8*2.6 = 25.48 m/s.
b. d = Vo*t + (g/2)*t^2.
d = 0 + 4.9*(2.6)^2 = 33.12 m.
0*(2.6) + (9.8/2) * (2.6)^2
To determine the final velocity of Upton and the distance he will fall while riding the Giant Drop at Great America, we need to use the equations of motion.
1. The first equation relates the final velocity (Vf) with the initial velocity (Vi), acceleration (a), and time (t):
Vf = Vi + at
Since Upton is free falling, his initial velocity is 0 m/s (assuming there is no initial upward thrust).
2. The second equation relates the distance (d) with the initial velocity, time, and acceleration:
d = Vi * t + 0.5 * a * t^2
Since the initial vertical velocity is 0 m/s, the equation simplifies to:
d = 0.5 * a * t^2
where 'a' is the acceleration due to gravity, which is approximately -9.8 m/s^2 (negative because it acts downwards).
Now, we can substitute the given values into these equations to find the final velocity and the distance Upton will fall.
1. Final Velocity:
Vf = 0 + (a * t)
= (-9.8 m/s^2) * (2.6 s)
= -25.48 m/s
Therefore, the final velocity of Upton will be approximately -25.48 m/s. Note that the negative sign indicates that the final velocity is downwards.
2. Distance:
d = 0.5 * a * t^2
= 0.5 * (-9.8 m/s^2) * (2.6 s)^2
≈ 0.5 * (-9.8 m/s^2) * 6.76 s^2
≈ -32.092 m
Therefore, Upton will fall approximately 32.092 meters. Again, the negative sign indicates that the displacement is downwards.
To summarize, Upton's final velocity will be approximately -25.48 m/s, and he will fall approximately 32.092 meters while riding the Giant Drop at Great America.