A fruit drops from the top of a tree 20m tall. The time it takes the fruit to reach the ground is
a=210m/s×s
what planet are you on? On earth, g = 10 m/s^2
s = 1/2 at^2
so, 5t^2 = 20
t = 2s
A=210m/s×s
Well, I hate to burst your fruit-filled bubble, but that equation doesn't quite add up. It looks like you mistakenly mixed up your units there. The equation a = 210 m/s × s seems to be missing some important information or it's just plain wrong. We need a bit more data to calculate the time it takes for the fruit to reach the ground. How about the initial velocity or acceleration? Let's crunch those numbers again, shall we?
To find the time it takes for the fruit to reach the ground, we can use the equation of motion:
s = ut + (1/2)at^2
where:
s = distance (20m, as the height of the tree)
u = initial velocity (0m/s, since the fruit is dropped)
a = acceleration due to gravity (-9.8m/s^2, considering downward direction)
t = time
Substituting the known values into the equation:
20 = (0)t + (1/2)(-9.8)t^2
Simplifying the equation:
10t^2 = 20
Dividing both sides by 10:
t^2 = 2
Taking the square root of both sides:
t = √2
Therefore, the time it takes for the fruit to reach the ground is approximately √2 seconds.
To determine the time it takes for the fruit to reach the ground, we can use the kinematic equation for vertical motion:
s = ut + (1/2)at^2
In this equation, s represents the displacement (change in height), u represents the initial velocity (which is zero in this case since the fruit is dropped), a represents the acceleration due to gravity (approximately 9.8 m/s^2), and t represents the time.
In this case, the initial velocity u is 0, the acceleration due to gravity a is -9.8 m/s^2 (negative because it acts in the opposite direction of the positive direction), and the displacement s is -20 m (negative because the fruit is falling downward).
Plugging these values into the equation, we have:
-20 = 0*t + (1/2)*(-9.8)*t^2
Simplifying the equation, we get:
-20 = -4.9*t^2
Dividing both sides by -4.9, we have:
t^2 = 20/4.9
Taking the square root of both sides, we have:
t ≈ √(20/4.9)
Calculating this approximate value, we get:
t ≈ √(4.081632653061225)
t ≈ 2.020 m/s
Therefore, the time it takes for the fruit to reach the ground is approximately 2.02 seconds.