A stone is thrown 125 m high tower calculate time taken to reach the ground and final velocity
The height h of the stone is
h = 125 - 4.9t^2
assuming it was thrown horizontally. So when is h=0?
And of course, v = -9.8t
using the value of t above.
Study
To calculate the time taken to reach the ground and the final velocity, we can use the equations of motion.
First, let's consider the vertical motion of the stone:
The initial vertical velocity (u) is 0 m/s because the stone is thrown vertically upward from rest.
The vertical displacement (s) is -125 m because the stone falls downwards.
The acceleration due to gravity (g) is approximately 9.8 m/s².
Using the equation of motion:
s = ut + (1/2)gt²
Substituting the values:
-125 = 0*t + (1/2)*9.8*t²
Rearranging the equation, we get:
4.9t² = 125
Dividing both sides by 4.9, we have:
t² = 25
Taking the square root of both sides, we get:
t = 5 seconds
Therefore, the time taken for the stone to reach the ground is 5 seconds.
To calculate the final velocity (v), we can use the equation:
v = u + gt
Substituting the values:
v = 0 + 9.8 * 5
Calculating the expression:
v = 49 m/s
Therefore, the final velocity of the stone when it reaches the ground is 49 m/s.
To calculate the time taken to reach the ground and the final velocity, we can use equations of motion. The motion of the stone can be divided into two phases: upward motion and downward motion.
First, let's calculate the time taken for the stone to reach its highest point during the upward motion.
We know that the initial velocity (u) of the stone is 0 m/s (since it is thrown vertically upwards) and the final velocity (v) at the highest point is also 0 m/s (at the peak of the trajectory). The acceleration (a) due to gravity is -9.8 m/s² (negative because it acts in the opposite direction to the upward motion).
We can use the following equation of motion to calculate the time taken to reach the highest point:
v = u + at
Plugging in the values:
0 = 0 + (-9.8) * t
0 = -9.8t
t = 0
This means that it takes 0 seconds for the stone to reach the highest point during the upward motion.
Next, let's calculate the time taken for the stone to fall from the highest point to the ground during the downward motion.
Since the stone is initially at rest at the highest point, its initial velocity (u) is 0 m/s. The acceleration (a) due to gravity remains at -9.8 m/s², but now acting downward.
We can use the following equation of motion to calculate the time taken for the stone to reach the ground:
s = ut + (1/2) * a * t^2
Here, s is the distance traveled, which is equal to 125 m (height of the tower), u is the initial velocity (0 m/s), a is the acceleration (-9.8 m/s²), and t is the time taken.
Plugging in the values:
125 = 0 + (1/2) * (-9.8) * t^2
125 = -4.9t^2
t^2 = -125 / -4.9
t^2 = 25.51
t ≈ √25.51
t ≈ 5.05 seconds
So, the time taken for the stone to reach the ground is approximately 5.05 seconds.
Finally, to calculate the final velocity (v) when the stone reaches the ground, we can use the equation of motion:
v = u + at
Plugging in the values:
v = 0 + (-9.8) * 5.05
v ≈ -49.49 m/s
The negative sign indicates that the velocity is directed downward.
Therefore, the stone will reach the ground in approximately 5.05 seconds and will have a final velocity of approximately -49.49 m/s.