Stone is thrown vertically downward with an inital speed of 2.0m/s from height of 10m, determine time it takes to reach the bottom.
Thanks!
h(t) = 10.0 - 2.0t - 4.9t^2
now just find t when h=0
To determine the time it takes for the stone to reach the bottom, we can use the concept of free fall motion and the equations of motion. In this case, the stone is thrown vertically downward, implying that it is accelerating due to gravity.
First, we need to understand that the acceleration due to gravity near the surface of the Earth is approximately -9.8 m/s^2 (negative sign indicates downward acceleration).
We can use the following equation of motion to find the time taken (t):
h = ut + (1/2)gt^2
Where:
h = height (in this case, 10 m)
u = initial velocity (in this case, -2.0 m/s, since it is thrown downward)
g = acceleration due to gravity (approximately -9.8 m/s^2)
t = time taken
Plugging in the given values into the equation, we have:
10 = (-2.0)t + (1/2)(-9.8)t^2
Simplifying this equation, we get:
10 = -2.0t - 4.9t^2
Rearranging the equation, we have a quadratic equation in the form of:
4.9t^2 + 2.0t - 10 = 0
To solve this equation, you can use the quadratic formula:
t = (-b ± √(b^2 - 4ac))/(2a)
In this case, a = 4.9, b = 2.0, and c = -10.
Plugging these values into the quadratic formula, we can find the time it takes for the stone to reach the bottom.