QuestionJuly 3, 2025

A small sports car and a pickup truck start coasting down a 17.0 m hill together,side by side. Assuming no friction, what is the velocity of each vehicle at the bottom of the hill? Assume that energy losses due to friction are negligible for both vehicles. v_(car)=square (m)/(s) eta ruck=square (m)/(s)

A small sports car and a pickup truck start coasting down a 17.0 m hill together,side by side. Assuming no friction, what is the velocity of each vehicle at the bottom of the hill? Assume that energy losses due to friction are negligible for both vehicles. v_(car)=square (m)/(s) eta ruck=square (m)/(s)
A small sports car and a pickup truck start coasting down a 17.0 m hill together,side by side. Assuming no friction, what is the velocity of each vehicle at the bottom of the hill? Assume that energy losses due to friction are negligible for both vehicles. v_(car)=square (m)/(s) eta ruck=square (m)/(s)

Solution
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Answer

v_{car} = v_{truck} = 18.3 \, \text{m/s} Explanation 1. Apply Conservation of Energy The potential energy at the top is converted to kinetic energy at the bottom. **Potential Energy (PE) = mgh** and **Kinetic Energy (KE) = \frac{1}{2}mv^2**. 2. Equate Potential and Kinetic Energy At the top, PE = mgh. At the bottom, KE = \frac{1}{2}mv^2. Set them equal: \(mgh = \frac{1}{2}mv^2\). 3. Solve for Velocity Cancel mass (m) from both sides: \(gh = \frac{1}{2}v^2\). Solve for v: \(v = \sqrt{2gh}\). 4. Calculate Velocity Substitute g = 9.8 \, \text{m/s}^2 and h = 17.0 \, \text{m}: \(v = \sqrt{2 \times 9.8 \times 17.0}\).

Explanation

1. Apply Conservation of Energy<br /> The potential energy at the top is converted to kinetic energy at the bottom. **Potential Energy (PE) = mgh** and **Kinetic Energy (KE) = \frac{1}{2}mv^2**.<br /><br />2. Equate Potential and Kinetic Energy<br /> At the top, PE = mgh. At the bottom, KE = \frac{1}{2}mv^2. Set them equal: \(mgh = \frac{1}{2}mv^2\).<br /><br />3. Solve for Velocity<br /> Cancel mass (m) from both sides: \(gh = \frac{1}{2}v^2\). Solve for v: \(v = \sqrt{2gh}\).<br /><br />4. Calculate Velocity<br /> Substitute g = 9.8 \, \text{m/s}^2 and h = 17.0 \, \text{m}: \(v = \sqrt{2 \times 9.8 \times 17.0}\).
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