A certain freely falling object, released from rest, requires 2.00 s to travel the last 33.0 m before it hits the ground.
(a) Find the velocity of the object when it is 33.0 m above the ground. (Indicate the direction with the sign of your answer. Let the positive direction be upward.)
m/s
(b) Find the total distance the object travels during the fall.
To find the velocity of the object when it is 33.0 m above the ground, we can use the equation of motion for freely falling objects:
v = u + at
Where:
v = final velocity (unknown)
u = initial velocity (0 m/s since it was released from rest)
a = acceleration due to gravity (-9.8 m/s^2 since it is in the downward direction)
t = time taken to travel the given distance (2.00 s)
Using the equation, we can calculate the final velocity:
v = 0 + (-9.8) * 2.00
v = -19.6 m/s
The negative sign indicates that the velocity is in the downward direction.
Therefore, the velocity of the object when it is 33.0 m above the ground is -19.6 m/s.
To find the total distance the object travels during the fall, we need to calculate the distance covered during the first part of the fall and add it to the given distance.
The distance covered during the first part of the fall can be calculated using the equation of motion:
d = ut + (1/2)at^2
Where:
d = distance covered during the first part of the fall (unknown)
u = initial velocity (0 m/s)
a = acceleration due to gravity (-9.8 m/s^2)
t = time taken to travel the given distance (2.00 s)
Using the equation, we can calculate the distance covered during the first part of the fall:
d = 0 * 2.00 + (1/2) * (-9.8) * (2.00)^2
d = -19.6 m
Since the distance is negative, it indicates that the object has traveled 19.6 m upward before falling down.
The total distance traveled during the fall is the sum of the given distance (33.0 m) and the distance covered during the first part of the fall:
Total distance = 33.0 + 19.6 = 52.6 m
Therefore, the total distance the object travels during the fall is 52.6 m.