QuestionMay 4, 2025

A block slides down a frictionless inclined ramp. If the ramp angle is 8.9^circ and its length is 24.0 m find the speed of the block as it reaches the bottom of the ramp, assuming it started sliding from rest at the top. Round your final answer to two decimal places and enter only the numerical value. Your answer should be in units of m/s

A block slides down a frictionless inclined ramp. If the ramp angle is 8.9^circ and its length is 24.0 m find the speed of the block as it reaches the bottom of the ramp, assuming it started sliding from rest at the top. Round your final answer to two decimal places and enter only the numerical value. Your answer should be in units of m/s
A block slides down a frictionless inclined ramp. If the ramp angle is 8.9^circ and its length is 24.0 m find the speed of the block as it reaches the bottom of the ramp, assuming it started sliding from rest at the top. Round your final answer to two decimal places and enter only the numerical value. Your answer should be in units of m/s

Solution
4.7(282 votes)

Answer

6.53 Explanation 1. Calculate gravitational acceleration component The component of gravitational acceleration along the ramp is g \sin(\theta), where g = 9.81 \, \text{m/s}^2 and \theta = 8.9^\circ. So, a = 9.81 \times \sin(8.9^\circ). 2. Use kinematic equation to find final speed Use **v^2 = u^2 + 2as** where initial speed u = 0, a is the acceleration from Step 1, and s = 24.0 \, \text{m} is the distance. Solve for v: v = \sqrt{2as}.

Explanation

1. Calculate gravitational acceleration component<br /> The component of gravitational acceleration along the ramp is $g \sin(\theta)$, where $g = 9.81 \, \text{m/s}^2$ and $\theta = 8.9^\circ$. So, $a = 9.81 \times \sin(8.9^\circ)$.<br /><br />2. Use kinematic equation to find final speed<br /> Use **$v^2 = u^2 + 2as$** where initial speed $u = 0$, $a$ is the acceleration from Step 1, and $s = 24.0 \, \text{m}$ is the distance. Solve for $v$: $v = \sqrt{2as}$.
Click to rate:

Similar Questions