A person on an icy expedition is trying to lower a crate of mass mị = 5.65 kg crate to the bottom of a steep ravine of height hz = 21.8 m using a rope over a simple pulley. The person, who m2 frictionless weighs m2 = 60.9 kg, is being careful to lower the crate at a constant speed of 1.50 m/s. Unfortunately, when the crate reaches a point h = 12.1 meters above the ground, the person h2 slips and the crate immediately accelerates toward the ground, dragging the hapless person across the ice and toward the edge of the cliff. If we assume the ice is perfectly slick (that is, no friction between the person and the ice once he slips and falls down), at what speed will the crate hit the ground? Assume also that the rope is long enough to allow the crate to hit the ground before the crewman slides over the side of the cliff. speed: m/s At what speed will the person hit the bottom of the ravine? (Assume no air friction.) speed: m/s
A person on an icy expedition is trying to lower a crate of mass mị = 5.65 kg crate to the bottom of a steep ravine of height hz = 21.8 m using a rope over a simple pulley. The person, who m2 frictionless weighs m2 = 60.9 kg, is being careful to lower the crate at a constant speed of 1.50 m/s. Unfortunately, when the crate reaches a point h = 12.1 meters above the ground, the person h2 slips and the crate immediately accelerates toward the ground, dragging the hapless person across the ice and toward the edge of the cliff. If we assume the ice is perfectly slick (that is, no friction between the person and the ice once he slips and falls down), at what speed will the crate hit the ground? Assume also that the rope is long enough to allow the crate to hit the ground before the crewman slides over the side of the cliff. speed: m/s At what speed will the person hit the bottom of the ravine? (Assume no air friction.) speed: m/s
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Transcribed Image Text:**Problem Statement:**
A person on an icy expedition is trying to lower a crate of mass \( m_1 = 5.65 \, \text{kg} \) to the bottom of a steep ravine of height \( h_2 = 21.8 \, \text{m} \) using a rope over a simple pulley. The person, who weighs \( m_2 = 60.9 \, \text{kg} \), is being careful to lower the crate at a constant speed of \( 1.50 \, \text{m/s} \). Unfortunately, when the crate reaches a point \( h = 12.1 \, \text{meters} \) above the ground, the person slips and the crate immediately accelerates toward the ground, dragging the hapless person across the ice and toward the edge of the cliff.
If we assume the ice is perfectly slick (that is, no friction between the person and the ice once he slips and falls down), at what speed will the crate hit the ground? Assume also that the rope is long enough to allow the crate to hit the ground before the crewman slides over the side of the cliff.
**Diagram Explanation:**
The diagram shows a simple pulley system with a person labeled \( m_2 \) standing on frictionless ice at the top of a cliff. A rope runs from the person over a pulley at the edge of the cliff to a crate labeled \( m_1 \). The height from the top of the cliff to the ground is labeled \( h_2 \), and the current height of the crate above the ground is labeled \( h \). The cliff edge and pulley are depicted in grey, indicating a slick, frictionless surface.
**Questions:**
1. At what speed will the crate hit the ground?
- **Speed:** _________ m/s
2. At what speed will the person hit the bottom of the ravine? (Assume no air friction.)
- **Speed:** _________ m/s
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