A tower is 88m high a stone is thrown vertically upward from the top of the tower with a velocity 2m/s The stone reach the ground after how many seconds?
using your basic equation of motion, the height h at time t is
h(t) = 88 + 2t - 4.9t^2
so, just find t when h=0
To find out how long it takes for the stone to reach the ground, we need to use the equations of motion.
First, let's list the known variables:
Initial velocity (u) = 2 m/s (upward, since the stone is thrown vertically upward)
Acceleration (a) = -9.8 m/s^2 (downward, due to gravity)
Final velocity (v) = ?
Displacement (s) = -88 m (negative because the stone is moving downward)
We can use the second equation of motion:
v^2 = u^2 + 2as
Since we want to find the time taken (t), we rearrange the equation to solve for time:
s = ut + 0.5at^2
Substituting the values into the equation, we have:
-88 = (2)t + 0.5(-9.8)t^2
Rearranging and simplifying the equation further:
-9.8t^2 + 2t - 88 = 0
This is a quadratic equation. We can solve for t by factoring, completing the square, or using the quadratic formula. In this case, let's use the quadratic formula:
t = (-b ± √(b^2 - 4ac)) / (2a)
Using the formula, substituting the values of a, b, and c:
t = (-(2) ± √((2)^2 - 4(-9.8)(-88))) / (2(-9.8))
Simplifying further:
t = (-2 ± √(4 - 3432)) / (-19.6)
Calculating the discriminant:
t = (-2 ± √(-3428)) / (-19.6)
Since the discriminant is negative, it implies that the stone will not reach the ground. It will, however, reach a maximum height and then fall back down.
Therefore, there is no real solution for t, indicating that the stone will not reach the ground.