The speed of a falling object is directly proportional to the time for which it falls. The speed after 5 seconds is 49 metres/seconds. What is the speed of an object which falls for 8 seconds?
x/8 = 49/5
To solve this problem, we can use a proportionality relationship between speed and time. Let's set up an equation using the information given:
Speed = constant * time
We're told that the speed after 5 seconds is 49 meters/second. Let's use this information to find the constant:
49 = constant * 5
To find the constant, we divide both sides of the equation by 5:
constant = 49 / 5
constant = 9.8
Now that we have the constant, we can determine the speed of an object that falls for 8 seconds using the equation:
Speed = constant * time
Speed = 9.8 * 8
Speed = 78.4 meters/second
Therefore, the speed of an object that falls for 8 seconds is 78.4 meters/second.
To solve this problem, we can use the given information and set up a proportion between time and speed.
We are told that the speed of a falling object is directly proportional to the time for which it falls. This can be written as:
Speed ∝ Time
Now, let's use the given information to find the constant of proportionality. We know that when the object falls for 5 seconds, the speed is 49 meters/second. Therefore, we can write:
Speed = k * Time
Where "k" is the constant of proportionality. Plugging in the values we have:
49 = k * 5
To find the value of "k," we divide both sides of the equation by 5:
k = 49 / 5
k = 9.8
Now that we have the value of "k," we can use it to find the speed of the object when it falls for 8 seconds. Using the equation we derived earlier:
Speed = k * Time
Plugging in the values:
Speed = 9.8 * 8
Speed = 78.4 meters/second
Therefore, the speed of the object after falling for 8 seconds is 78.4 meters/second.