Two diamonds begin a free fall from rest from the same height 0.9 s apart. How long after the first object begins to fall will the two objects be 11 m apart?
An ostrich can run at speeds of up to 72 km/h. How long will it take an ostrich to run 1.5 km at this top speed?
To solve this problem, we need to understand the motion of the objects and the concept of free fall.
When an object is in free fall, it is only affected by the force of gravity. The acceleration due to gravity, denoted as "g," is approximately equal to 9.8 m/s^2 near the surface of the Earth.
Let's break down the problem into steps:
Step 1: Find the time it takes for the first object to fall from the initial height to the desired distance.
Using the equation for motion under constant acceleration, we can find the time it takes for an object to fall a certain distance. The equation is:
d = (1/2) * g * t^2
Where:
- d is the distance
- g is the acceleration due to gravity
- t is the time
Rearranging the equation, we can solve for time:
t = √(2d/g)
Given that the distance is 11 m and the acceleration due to gravity is 9.8 m/s^2, we can plug in the values:
t = √(2 * 11 / 9.8)
t = √2.244
t ≈ 1.497 s (rounded to three decimal places)
Therefore, it takes approximately 1.497 seconds for the first object to fall 11 m.
Step 2: Find the time it takes for the second object to fall from the same initial height to the desired distance.
Since the second object starts falling 0.9 seconds after the first object, we need to subtract 0.9 seconds from the time it takes for the first object to fall.
t2 = t1 - 0.9
t2 ≈ 1.497 - 0.9
t2 ≈ 0.597 s (rounded to three decimal places)
Therefore, it takes approximately 0.597 seconds for the second object to fall 11 m after the first object begins to fall.
To summarize, the second object will be 11 m apart from the first object approximately 0.597 seconds after the first object begins to fall.