Henry tossed up a ball with an initial velocity of 19.6m/s It will take square to reach the maximum height. If he climbs a 20 m high cliff and toss the ball upwards with same inthal velocity of 19.6m/s it will reach the ground after square

To solve this problem, we kinematic equations of motion under constant acceleration due to gravity.<br /><br />1. Time to reach the maximum height when tossed from the ground:<br /><br />Given:<br />- Initial velocity, \( v_0 = 19.6 \, \text{m/s} \)<br />- Acceleration due to gravity, \( g = 9.8 \, \text{m/s}^2 \)<br /><br />The time to reach the maximum height can be found using the equation:<br />\[ t_{\text{max height}} = \frac{v_0}{g} \]<br /><br />Substituting the given values:<br />\[ t_{\text{max height}} = \frac{19.6 \, \text{m/s}}{9.8 \, \text{m/s}^2} = 2 \, \text{s} \]<br /><br />So, it will take 2 seconds to reach the Time to reach the ground when tossed from a 20 m high cliff:<br /><br />Given:<br />- Initial velocity, \( v_0 = 19.6 \, \text{m/s} \)<br />- Height of the cliff, \( h = 20 \, \text{m} \)<br />- Acceleration due to gravity, \( g = 9.8 \, \text{m/s}^2 \)<br /><br />The total time to reach the ground can be found using the equation:<br />\[ t_{\text{ground}} = \frac{v_0 + \sqrt{v_0^2 + 2gh}}{g} \]<br /><br />Substituting the given values:<br />\[ t_{\text{ground}} = \frac{19.6 \, \text{m/s} + \sqrt{(19.6/s})^2 + 2 \9.8 \, \text{m/s}^2 \cdot 20 \, \text{m}}}{9.8 \, \text{m/s}^2} \]<br /><br />First, calculate the term inside the square root:<br />\[ (19.6 \, \text{m/s})^2 + 2 \cdot 9.8 \, \text{m/s}^2 \cdot 20 \, \text{m} = 384.16 \, \text{m}^2/\text{s}^2 + 392 \, \text{m}^2/\text{s}^2 = 776.16 \, \text{m}^2/\text{s}^2 \]<br /><br />Now, take the square root:<br />\[ \sqrt{776.16 \,^2/\text{s}^2} = 27.83 \, \text{m/s} \]<br /><br />Finally, substitute back into the equation:<br />\[ t_{\text{ground}} = \frac{19.6 \, \text{m/s} + 27.83 \, \text{m/s}}{9.8 \, \text{m/s}^2} = \frac{47.43 \, \text{m/s}}{9.8 \, \text{m/s}^2} = 4.83 \, \text{s} \]<br /><br />So, it will take approximately 4.83 seconds to reach the ground when tossed from the 20 m high cliff.<br /><br />Therefore, the answers are:<br />- It will take 2 seconds to reach the maximum height.<br />- It will take approximately the ground when tossed from the 20 m high cliff.