A construction worker drops a hammer from a height of 25 m.
How long will it take the hammer to hit the ground?
Use the formula h(t)=−4.9t62+vot+ho , where vo is the initial velocity and ho is the initial height.
Round to the nearest tenth of a second.
Enter your answer in the box.
For anyone stuck on the question the answer is 2.3 seconds.
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Answer it
Well, if a construction worker drops a hammer from a height of 25 m, it won't take too long for it to hit the ground -- probably a lot less time than it took for me to come up with this clever response! But let's do the math to figure out exactly how long it will take.
Using the formula h(t) = -4.9t^2 + vot + ho, we know that the initial height (ho) is 25m, and since the hammer is dropped, the initial velocity (vo) is 0 m/s. So the formula becomes h(t) = -4.9t^2 + 25.
Now, we need to find the time it takes for the hammer to hit the ground, which is when h(t) = 0. So, let's set the equation to 0:
0 = -4.9t^2 + 25.
To solve for t, we'll rearrange the equation and solve the quadratic equation:
4.9t^2 = 25,
t^2 = 25/4.9,
t = √(25/4.9).
Calculating that, we find t ≈ 2.033 seconds.
So, to the nearest tenth of a second, it will take about 2.0 seconds for the hammer to hit the ground and make a "ground-breaking" appearance.
To find out how long it will take for the hammer to hit the ground, we can use the formula h(t) = -4.9t^2 + vot + ho.
In this case, the initial height (ho) is 25 meters, and we can assume that the initial velocity (vo) is zero since the hammer is just dropped.
Now we can substitute these values into the formula:
h(t) = -4.9t^2 + 0t + 25
Since we want to find the time it takes for the hammer to hit the ground, we set h(t) equal to zero:
0 = -4.9t^2 + 25
Rearranging the equation, we have:
4.9t^2 = 25
Dividing both sides of the equation by 4.9, we get:
t^2 = 5.1
Now we take the square root of both sides to solve for t:
t = √5.1 ≈ 2.26
So, it will take approximately 2.3 seconds for the hammer to hit the ground when dropped from a height of 25 meters.
so, solve
25-4.9t^2 = 0