Galileo, in his book Two new sciences, stated that for elevations that exceed or fall short of \(45^\circ\) by equal amounts, the ranges:
1. | are equal to each other. |
2. | are not equal to each other. |
3. | are sometimes equal and sometimes not equal to each other. |
4. | depends on the difference between the angles. |
A hiker stands on the edge of a cliff \(490~\mathrm{m}\) above the ground and throws a stone horizontally with an initial speed of \(15\) m/s. Neglecting air resistance, the time taken by the stone to reach the ground and the speed with which it hits the ground are, respectively: (Take \(g=9.8~\mathrm{m/s^2}\))
1. | \(10\) s and \(99\) m/s |
2. | \(10\) s and \(15\) m/s |
3. | \(5\) s and \(99\) m/s |
4. | \(5\) s and \(15\) m/s |
A cricket ball is thrown at a speed of \(28\) m/s in a direction \(30^\circ\) above the horizontal. The time taken by the ball to return to the same level is:
1. \(2.5\) s
2. \(2.9\) s
3. \(3.5\) s
4. \(3\) s
A cricket ball is thrown at a speed of \(28\) m/s in a direction \(30^{\circ}\) above the horizontal. The maximum height attained by the ball is:
1. \(5\) m
2. \(10\) m
3. \(15\) m
4. \(20\) m