Solving Motion in 2 Dimensions: Hammer Dropped from 10m Roof

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In summary, the hammer travels a horizontal distance of 2.69 meters between the time it leaves the roof and the time it hits the ground.
  • #1
Beretta
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A worker on the roof of a house drops her hammer which slides down the roof at constant speed of 4m/s. Th roof makes an angle of 30 with the horizontal, and the lowest point is 10m from the ground. what is the the horizontal distance traveled by the hammer between the time is leaves the roof of the house and the time it hits the ground?

What happen here is that I assumed that theta is 60 since it makes an angle if 30 with the horizontal and since the object is sliding down. Thus it leaves the roof on a 60 degree angle.

vx = 4m/s cos 60 = 2m/s
vy = 4m/s sin 60 = 3.46m/s

x(t) = x0 + vxt

y(t) = y0 + v0t - (1/2)g(t^2)
10m - 3.46m/s(t) + (0.5)(9.81m/s^2)t^2 = 0

I am ending up with a negative root Delta.
May you help me pls?
 
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  • #2
The horizontal distance traveled by the hammer is found using the x equation: x(t) = x0 + vxt. Since the hammer is initially at the roof, x0 = 0 and vx = 2m/s, so the equation becomes x(t) = 2m/s t. To find t, we solve the y equation for t: 10m - 3.46m/s(t) + (0.5)(9.81m/s^2)t^2 = 0. This gives us t = 1.345 seconds. So, the horizontal distance traveled by the hammer is x(t) = 2m/s * 1.345s = 2.69 m.
 

1. What is the equation for solving motion in 2 dimensions?

The equation for solving motion in 2 dimensions is d = v0t + 1/2at2, where d is the displacement, v0 is the initial velocity, a is the acceleration, and t is the time.

2. How do I find the initial velocity of an object dropped from a height?

To find the initial velocity of an object dropped from a height, you can use the equation v0 = √(2gh), where g is the acceleration due to gravity (9.8 m/s2) and h is the height.

3. Can I assume the acceleration is constant for an object dropped from a height?

Yes, in most cases, the acceleration due to gravity can be assumed to be constant (9.8 m/s2) for objects dropped from a height on Earth.

4. What is the relationship between the horizontal and vertical components of an object's velocity?

The horizontal and vertical components of an object's velocity are independent of each other. This means that the horizontal velocity remains constant while the vertical velocity changes due to acceleration from gravity.

5. How do I calculate the time it takes for an object to reach the ground after being dropped from a height?

You can use the equation t = √(2h/g), where h is the height and g is the acceleration due to gravity, to calculate the time it takes for an object to reach the ground after being dropped from a height.

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