If two objects weighing 5 kg and 7 kg are dropped from a height of 64 m and 36 m, respectively. What will be the ratio of times taken to reach the ground?
Thanks.
To find the ratio of the times taken by the two objects to reach the ground, we can use the equation of motion:
h = 1/2 * g * t^2
where h is the height, g is the acceleration due to gravity, and t is the time taken.
Let's find the time taken by the first object weighing 5 kg:
h1 = 64 m
g = 9.8 m/s^2
Using the equation of motion:
64 = 1/2 * 9.8 * t1^2
Simplifying the equation:
t1^2 = 64 / (1/2 * 9.8)
t1^2 = 64 / 4.9
t1^2 = 13.06
t1 ≈ √13.06
t1 ≈ 3.61 seconds
Now, let's find the time taken by the second object weighing 7 kg:
h2 = 36 m
Using the equation of motion:
36 = 1/2 * 9.8 * t2^2
Simplifying the equation:
t2^2 = 36 / (1/2 * 9.8)
t2^2 = 36 / 4.9
t2^2 = 7.35
t2 ≈ √7.35
t2 ≈ 2.71 seconds
The ratio of the times taken to reach the ground is t1/t2:
t1/t2 = 3.61/2.71 ≈ 1.33 (rounded to two decimal places)
Therefore, the ratio of the times taken to reach the ground for the two objects is approximately 1.33:1.
To find the ratio of times taken for two objects to reach the ground, we need to calculate the time it takes for each object to fall from their respective heights.
The time taken for an object to fall from a height can be determined using the formula:
t = √(2h/g)
Where:
t = time taken to fall
h = height
g = acceleration due to gravity (which is approximately 9.8 m/s^2 on Earth)
Let's calculate the time taken for each object separately:
For the object weighing 5 kg:
Height (h) = 64 m
Using the formula, we can calculate the time (t1) taken for this object to reach the ground:
t1 = √(2 * 64 / 9.8)
For the object weighing 7 kg:
Height (h) = 36 m
Using the same formula, we can calculate the time (t2) taken for this object to reach the ground:
t2 = √(2 * 36 / 9.8)
Now, we can find the ratio of times taken for both objects to reach the ground:
Ratio = t1 / t2
By substituting the values of t1 and t2 in the above formula, we can calculate the required ratio.
h=1/2 g*t^2
t=sqrt(2h/g)
ratio= sqrt(64/36)