To find the time of motion and velocity when an object hits the ground after being dropped from a height of 320 meters, we can use the equations of motion under constant acceleration due to gravity.
The equation for calculating the time taken for an object to fall freely from a height h is:
h = (1/2) * g * t^2
Where: h = initial height (320 m) g = acceleration due to gravity (approximately 9.8 m/s^2) t = time of motion
Rearranging the equation, we have:
t^2 = (2h) / g
Substituting the values, we get:
t^2 = (2 * 320) / 9.8 t^2 = 64.89795918
Taking the square root of both sides, we find:
t ≈ 8.06 seconds (rounded to two decimal places)
So, the time of motion when the object hits the ground is approximately 8.06 seconds.
To calculate the velocity of the object when it hits the ground, we can use the equation:
v = g * t
Substituting the values, we have:
v = 9.8 * 8.06 v ≈ 79.388 m/s (rounded to three decimal places)
Therefore, the velocity of the object when it hits the ground is approximately 79.388 m/s.