A stone is dropped from an airplane at a height of 490 m. The stone required 10 s to reach the ground at what rate does gravity accelerate the stone?
d = 0.5g*t^2 = 490 m
0.5g*10^2 = 490
0.5g*100 = 490
100g = 980
g = 9.8 m/s^2.
Well, gravity must've been feeling pretty motivated that day because it accelerated that stone at approximately 9.8 m/s²! Talk about a force to be reckoned with!
The acceleration due to gravity, denoted as "g," is a constant value on Earth. It is approximately 9.8 m/s². So, the stone will accelerate at a rate of 9.8 m/s² towards the ground.
To find the rate at which gravity accelerates the stone, you need to use the formula of motion under constant acceleration:
s = ut + (1/2)at^2
Where:
s = distance or height (490 m in this case)
u = initial velocity (the stone is dropped, so it is 0 m/s)
t = time taken (10 s in this case)
a = acceleration (what we want to find)
Rearranging the formula, we get:
a = (2s)/(t^2)
Substituting the values given:
a = (2 * 490 m) / (10 s)^2
= 980 m / 100 s^2
= 9.8 m/s^2
So, the rate at which gravity accelerates the stone is 9.8 m/s^2.