Use the position equation given below, where s represents the height of the object (in feet), v0 represents the initial velocity of the object (in feet per second), s0 represents the initial height of the object (in feet), and t represents the time (in seconds), as the model for the problem.
s = –16t2 + v0t + s0
You drop a coin from the top of a building that has a height of 972 feet.
(c) How long will it take before the coin strikes the ground? (Round your answer to 2 decimal places.)
sec
Well, to find out how long it will take before the coin strikes the ground, we need to set the height (s) to 0, since the ground is at zero height. So, we have:
0 = -16t^2 + v0t + s0
In this case, since we dropped the coin from rest, there is no initial velocity (v0), and the initial height (s0) is the height of the building, which is 972 feet.
Now, let's plug in the values:
0 = -16t^2 + 972
To solve for t, we need to isolate t on one side of the equation. So, let's rearrange the equation:
16t^2 = 972
Now divide both sides by 16:
t^2 = 60.75
To find t, we take the square root of both sides:
t ≈ 7.8
Therefore, it will take approximately 7.8 seconds before the coin strikes the ground. And just a friendly reminder, always be ready to catch it. You don't want to drop the ball... or the coin in this case!
To find the time it takes for the coin to strike the ground, we need to set the height (s) equal to zero and solve for t in the position equation.
Given:
s = 0 (since the coin is at the ground)
s0 = 972 (the initial height of the coin)
v0 = 0 (since the coin is dropped, the initial velocity is zero)
The position equation becomes:
0 = -16t^2 + 0t + 972
Simplifying the equation:
-16t^2 + 972 = 0
To solve for t, we can use the quadratic formula:
t = (-b ± √(b^2 - 4ac)) / (2a)
For this equation, a = -16, b = 0, and c = 972.
Plugging the values into the quadratic formula:
t = (-0 ± √(0^2 - 4(-16)(972))) / (2(-16))
t = (√(0 - (-62208))) / (-32)
t = (√(62208)) / (-32)
t = (√(6216*10)) / (-32)
t = (2√(1554))/ (-32)
t = (√1554)/ (-16)
Using a calculator, we find that √1554 ≈ 39.43.
Therefore, it will take approximately 39.43 seconds for the coin to strike the ground. (Rounded to 2 decimal places)
To find the time it takes for the coin to strike the ground, we need to determine when the height (s) becomes 0.
Given:
s = -16t^2 + v0t + s0
s0 = 972 feet (initial height of the coin)
v0 = 0 feet per second (the coin is dropped from rest)
Substituting the given values into the position equation:
0 = -16t^2 + 0t + 972
Now, we need to solve this equation for t.
Rearrange the equation:
16t^2 = 972
Divide both sides by 16:
t^2 = 972/16
Simplify:
t^2 = 60.75
Take the square root of both sides:
t = √60.75
Now, we can find the numerical value for t:
t ≈ 7.80 seconds
Therefore, it will take approximately 7.80 seconds for the coin to strike the ground.
since you "dropped" the coin , v = 0
so
s = 16t^2 + 972
when it hits the ground, s = 0
16t^2 = 972
t^2 = 60.75
t = √60.75 = appr 7.79 sec