What is the horizontal distance traveled by the hammer from the time it leaves the roof to the time it hits the ground?A worker on the roof of a house drops his 0.83kg hammer, which slides down the...

What is the horizontal distance traveled by the hammer from the time it leaves the roof to the time it hits the ground?

A worker on the roof of a house drops his 0.83kg hammer, which slides down the roof at constant speed of 8.55m/s. The roof makes an angle of 21 degrees with the horizontal, and its lowest point is 20.7m from the ground.

What is the horizontal distance traveled by the hammer from the time it leaves the roof to the time it hits the ground? The acceleration due to gravity is 9.8m/s^2.

Asked on by pavilion77

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The worker on the roof of the house drops his 0.83kg hammer, which slides down the roof at constant speed of 8.55m/s.

The angle made by the roof with the horizontal is 21 degrees and its lowest point is 20.7m from the ground.

The hammer after being dropped travels at a constant velocity due to the presence of friction. The deceleration due to the frictional force is equal to the acceleration due to the gravitational force acting on the hammer. Once the hammer leaves the edge of the roof, there is only an acceleration acting vertically downwards. The component of the velocity of the hammer when it leaves the edge can be divided into a vertical component equal to 8.55*sin 21 acting downwards and a horizontal component of 8.55*cos 21.

If the time taken by the hammer to fall 20.7 m is t, 8.55*sin 21*t + (1/2)*9.8*t^2 = 20.7

Solving the equation for t gives the positive root as 1.9198 s. In 1.9198 s, the hammer moves a horizontal distance equal to 8.55*cos 21*1.9198 = 15.32 m

The horizontal distance traveled by the hammer from the time it leaves the roof to the time it hits the ground is 15.32 m

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