a box is sliding along a frictionless surface and gets to a ramp. disregarding friction, how fast should the…

a box is sliding along a frictionless surface and gets to a ramp. disregarding friction, how fast should the box be going on the ground in order to slide up the ramp to a height of 2.5 meters, where it stops? (use g = 9.8 m/s².)\n2.2 m/s\n7.0 m/s\n9.9 m/s\n24 m/s

a box is sliding along a frictionless surface and gets to a ramp. disregarding friction, how fast should the box be going on the ground in order to slide up the ramp to a height of 2.5 meters, where it stops? (use g = 9.8 m/s².)\n2.2 m/s\n7.0 m/s\n9.9 m/s\n24 m/s

Answer

Answer:

B. 7.0 m/s

Explanation:

Step1: Apply energy - conservation

Initial kinetic energy $K_{i}=\frac{1}{2}mv_{i}^{2}$, final potential energy $U_{f}=mgh$. Since there is no friction, $K_{i}=U_{f}$.

Step2: Solve for initial velocity

$\frac{1}{2}mv_{i}^{2}=mgh$. Cancel out mass $m$ on both sides: $\frac{1}{2}v_{i}^{2}=gh$. Given $h = 2.5$ m and $g=9.8$ m/s², then $v_{i}=\sqrt{2gh}$.

Step3: Calculate the value

$v_{i}=\sqrt{2\times9.8\times2.5}=\sqrt{49}=7.0$ m/s.