a stone is thrown vertically upward with an initial velocity v0. the distance travelled by it in time 1.5v0/g
height= Vo*t-1/2 g t^2
put in for time t, 1.5 seconds, that gives you the height.
To determine the distance travelled by the stone in time 1.5v0/g, we need to break down the problem and analyze the motion of the stone.
Let's start with some basic concepts:
1. On Earth, any object experiences an acceleration due to gravity, denoted as 'g'. The magnitude of gravity is approximately 9.8 m/s².
2. When an object is thrown vertically upward, its initial velocity (v0) is positive. However, it starts to slow down due to the opposing force of gravity until it reaches the highest point of its trajectory.
Now, let's calculate the distance traveled by the stone in time 1.5v0/g:
1. First, we need to determine how long it takes for the stone to reach the highest point of its trajectory. At the highest point, the velocity of the stone becomes zero.
Using the equation for final velocity (vf) in vertical upward motion:
vf = v0 - g * t
Where:
vf = final velocity (0 m/s)
v0 = initial velocity of the stone
g = acceleration due to gravity
t = time taken to reach the highest point
Setting the final velocity to zero, we can solve for 't':
0 = v0 - g * t
t = v0/g
2. Now that we have the time taken to reach the highest point, we can calculate the time it takes for the stone to reach the distance of 1.5v0/g.
Given that distance = velocity * time, we can rearrange the equation to solve for time.
1.5v0/g = v0 * t
t = (1.5v0/g) / v0
t = 1.5/g
3. Finally, to calculate the distance traveled by the stone in time 1.5v0/g, we can use the equation for distance traveled (d):
d = v0 * t - (1/2) * g * t²
Substituting the value of 't' we calculated earlier:
d = v0 * (1.5/g) - (1/2) * g * (1.5/g)²
d = 1.5v0/g - (1/2) * g * (2.25/g²)
d = 1.5v0/g - 2.25/g
Hence, the distance traveled by the stone in time 1.5v0/g is (1.5v0/g - 2.25/g).