A mouse jumps horizontally from a box of height 0.25 m. If the mouse jumps with a speed of 2.1m/s how far from the box does the mouse land? A. 8.4 m B. 0.47 m C. 0.25 m D. 0.12 m

To solve this problem, we need to find the time it takes for the mouse to fall from the box and then use that time to calculate the horizontal distance it travels.<br /><br />Given:<br />- Initial vertical velocity (u) = 0 m/s (since the mouse jumps horizontally)<br />- Height of the box (h) = 0.25 m<br />- Horizontal speed (v) = 2.1 m/s<br /><br />First, we calculate the time (t) it takes for the mouse to fall using the formula for free fall:<br /><br />\[ h = \frac{1}{2} g t^2 \]<br /><br />where \( g \) is the acceleration due to gravity (approximately \( 9.8 \, \text{m/s}^2 \)).<br /><br />Rearranging the formula to solve for \( t \):<br /><br />\[ t = \sqrt{\frac{2h}{g}} \]<br /><br />Plugging in the values:<br /><br />\[ t = \sqrt{\frac{2 \times 0.25 \, \text{m}}{9.8 \, \text{m/s}^2}} \]<br /><br />\[ t = \sqrt{\frac{0.5 \, \text{m}}{9.8 \, \text{m/s}^2}} \]<br /><br />\[ t = \sqrt{0.0506 \, \text{s}^2} \]<br /><br />\[ t \approx 0.22 \, \text{s} \]<br /><br />Next, we use this time to find the horizontal distance (d) the mouse travels:<br /><br />\[ d = v \times t \]<br /><br />\[ d = 2.1 \, \text{m/s} \times 0.22 \, \text{s} \]<br /><br />\[ d \approx 0.462 \, \text{m} \]<br /><br />Therefore, the mouse lands approximately 0.47 meters from the box.<br /><br />The correct answer is:<br /><br />B. 0.47 m