A person stands on a bridge that is 100 feet above a river.
If she drops a pebble how fast is it moving after 2 seconds?
How long does it take the pebble to reach the river below?
She has another pebble that she tosses up with initial speed of 8 feet per second. It goes up, then starts falling down to the river below. By the time it reaches the river what is its speed?
see the other post
It will be 16ft in 2seconds
And 100 seconds reach the river
To answer these questions, we need to consider the basic principles of motion and the equations that govern it, particularly the equations of motion under constant acceleration.
1. How fast is the pebble moving after 2 seconds?
We can find the answer using the equation for velocity. Assuming the pebble is dropped from rest, the equation for the velocity at any time (t) is given by:
v = u + at
where:
v = final velocity
u = initial velocity (which is 0 for a dropped object)
a = acceleration (which is the acceleration due to gravity, approximately 32.2 feet per second squared)
Applying the values, we have:
v = 0 + (32.2 ft/s^2)(2 s)
v = 64.4 ft/s
Therefore, the pebble is moving at a velocity of 64.4 feet per second after 2 seconds.
2. How long does it take the pebble to reach the river below?
To find the time it takes for the pebble to reach the river below, we can use the equation for time. Assuming the pebble starts from rest at 100 feet above the river and the acceleration due to gravity remains constant, we can use the following equation derived from the equation of motion:
s = ut + (1/2)at^2
where:
s = displacement (distance covered, which is -100 ft in this case because the pebble is falling downward)
u = initial velocity (0 ft/s)
a = acceleration (-32.2 ft/s^2)
t = time taken to reach the river (what we're trying to find)
Applying the values, we have:
-100 = 0 + (1/2)(-32.2 ft/s^2)t^2
-100 = -16.1t^2
t^2 = 100/16.1
t ≈ 3.12 seconds (rounded to two decimal places)
Therefore, it takes approximately 3.12 seconds for the pebble to reach the river below.
3. What is the speed of the pebble when it reaches the river?
To find the speed of the pebble when it reaches the river, we can use the equation for velocity, similarly to the first question. Assuming the initial velocity is positive (upwards) and the final velocity is negative (downwards), the equation becomes:
v = u + at
Applying the values, we have:
v = 0 + (-32.2 ft/s^2)(t)
v = -32.2t
Since we know it takes approximately 3.12 seconds for the pebble to reach the river, we can substitute this value into the equation:
v ≈ -(32.2 ft/s^2)(3.12 s)
v ≈ -100.6 ft/s
Therefore, the speed of the pebble when it reaches the river is approximately 100.6 feet per second downwards.