An object is dropped from rest from the top of a 400 m cliff on Earth. If air resistance is negligible, what is the distance the object travels during the first 6s of its fall?
a)30m
b)60m
c)120m
d)180m
e)360m
I got a) as my answer. I used
x-x_i = v_i * t +1/2at
x-400= 0(6) + 1/2 (9.8)(6)
x-400=29.4
x=429.4
so then I did 429.4-400 which gave me 29.4
Is this correct?
I don't know what you are trying to do with those equations. Try using the correct formula, which is
distance fallen = (1/2) g t^2.
None of the choices is quite right but (d0 is closest. Perhaps they expect you to assume that g = 10 m/s^2. The actual value is 9.8, which you have used.
Change in X = 1/2at^2 a=10 t=6
1/2(10)(36)= 1/2(360)= 180m
Ah, the age-old question of falling objects. Let me calculate that for you with a sprinkle of clownish humor!
Using the formula, distance fallen = (1/2) g t^2, and knowing that g = 9.8 m/s^2, let's plug in the numbers:
distance fallen = (1/2) * 9.8 * (6^2)
distance fallen = (1/2) * 9.8 * 36
distance fallen ≈ 176.4 m
So, it seems there was a little spill with your calculations. The correct answer would be closer to (d) 180m. Just a small discrepancy, but hey, no worries, math can be a bit slippery sometimes!
To find the distance the object travels during the first 6 seconds of its fall, we can use the formula:
distance fallen = (1/2)gt^2
Given that the object is dropped from rest, g (acceleration due to gravity) is 9.8 m/s^2 on Earth. So, plugging in the values:
distance fallen = (1/2)(9.8)(6)^2
distance fallen = (1/2)(9.8)(36)
distance fallen = 176.4 meters
Therefore, the correct answer is not listed among the options given. However, option (d) with 180 meters is the closest approximation.
To find the distance an object travels during the first 6 seconds of its fall, you can use the equation for the distance fallen:
distance = (1/2) * g * t^2,
where g is the acceleration due to gravity, t is the time, and distance is the distance fallen.
Plugging in the given values, g = 9.8 m/s^2 and t = 6 s, we can calculate the distance fallen:
distance = (1/2) * 9.8 * (6^2)
= 1/2 * 9.8 * 36
= 176.4 m.
None of the given choices match this value exactly, but the closest option is d) 180m. So, the correct answer is d) 180m.