- An athlete executing a long jump leaves the ground at angle `30^0` and travels `8.9` `m`. What was the take off speed?
- A bomber is flying horizontally at a speed of `72` `m`/`s` at the height of `100` `m` from the ground. When directly over the point `O` (located at `x = 0`), bomb `B` is released, which strikes the truck, which is moving along a level road (x-axis) with a constant velocity `v_2`. At the instant, the bomb is released, the truck is at a distance `x_0 = 125` `m` from `O`. Find the value of `v_2` and the time of flight.
- A ball rolls off from the top of a stairway with a horizontal velocity `u` `m`/`s`. If the steps are `h` metre high and `w` metre wide, show that the ball will just hit the edge of the nth step if `n = (2hu^2)/(gw^2)`
- A body is projected downward at an angle of `30^0` with the horizontal from the top of building `196` `m` high. Its initial speed is `60` `m`/`s`. How long will it take before striking the ground ? Also find how far from the foot of the building the body will strike and at what angle with horizontal ?
- A ball is projected vertical upward with a velocity of `29.4` `m`/`s`. At what instants of times, after projecion, it will be at height of `19.6` `m` from the ground?
- A projectile is released from a certain height on its way in downward direction. It crashes against and brakes a horizontal glass plate `5` `s` after it was released. It loses one third of its velocity during this crash. It takes a total time of `8` `s` to reach the ground. Determine the height from which it was released.
- Two particles are projected with the same initial velocity, one making an angle `theta` with the horizontal and other making angle `theta` with the vertical. If their common range is `R`, then determine the relationship of the product of their times of flight with `R`.
- Show that there are two values of time for same height during the cause of flight of projectile and the sum of timings at which these heights are attained is equal to the total time of flight.
- A fighter plane flying horizontally at an altitude of `1.5` `km` with speed `720` `km`/`h`, passes directly overhead an anti-craft gun. At what angle from the vertical should the gun be fired for the shell with muzzle speed `600` `m`/`s` to hit the plane?
- A player kicks a football at an angle `30^0` with the horizontal and with an initial velocity of `19.6` `m`/`s`. A second player standing at a distance of `20` `m` from the first player and in the direction of the kick, starts running to meet the ball at the instant the ball is kicked. How far and how fast must he run in order to catch the ball before it hits the ground?
- A ball of mass `m` is thrown vertically up, another ball of mass `2` `m` is thrown at an angle `theta`. If their times of ascent are equal. Find the heights attained by them in ratio form.
- From a point at a height `h` above the horizontal ground, a particle `A` is projected with a velocity `v_0` in an upward direction making an angle `theta` with the horizontal. Another particle `B` is also projected with the same velocity `v_0` from the same point but in downward direction opposite to `A`. Show that the two particles will strike the ground at a distance: `(2u)/g * cos theta * sqrt((v_0)^2 sin^2 theta + 2gh)`

**Recommended Lessons**

- An athlete executing a long jump leaves the ground at angle `30^0` and travels `8.9` `m`. What was the take off speed?
- A bomber is flying horizontally at a speed of `72` `m`/`s` at the height of `100` `m` from the ground. When directly over the point `O` (located at `x = 0`), bomb `B` is released, which strikes the truck, which is moving along a level road (x-axis) with a constant velocity `v_2`. At the instant, the bomb is released, the truck is at a distance `x_0 = 125` `m` from `O`. Find the value of `v_2` and the time of flight.
- A ball rolls off from the top of a stairway with a horizontal velocity `u` `m`/`s`. If the steps are `h` metre high and `w` metre wide, show that the ball will just hit the edge of the nth step if `n = (2hu^2)/(gw^2)`
- A body is projected downward at an angle of `30^0` with the horizontal from the top of building `196` `m` high. Its initial speed is `60` `m`/`s`. How long will it take before striking the ground ? Also find how far from the foot of the building the body will strike and at what angle with horizontal ?
- A ball is projected vertical upward with a velocity of `29.4` `m`/`s`. At what instants of times, after projecion, it will be at height of `19.6` `m` from the ground?
- A projectile is released from a certain height on its way in downward direction. It crashes against and brakes a horizontal glass plate `5` `s` after it was released. It loses one third of its velocity during this crash. It takes a total time of `8` `s` to reach the ground. Determine the height from which it was released.
- Two particles are projected with the same initial velocity, one making an angle `theta` with the horizontal and other making angle `theta` with the vertical. If their common range is `R`, then determine the relationship of the product of their times of flight with `R`.
- Show that there are two values of time for same height during the cause of flight of projectile and the sum of timings at which these heights are attained is equal to the total time of flight.
- A fighter plane flying horizontally at an altitude of `1.5` `km` with speed `720` `km`/`h`, passes directly overhead an anti-craft gun. At what angle from the vertical should the gun be fired for the shell with muzzle speed `600` `m`/`s` to hit the plane?
- A player kicks a football at an angle `30^0` with the horizontal and with an initial velocity of `19.6` `m`/`s`. A second player standing at a distance of `20` `m` from the first player and in the direction of the kick, starts running to meet the ball at the instant the ball is kicked. How far and how fast must he run in order to catch the ball before it hits the ground?
- A ball of mass `m` is thrown vertically up, another ball of mass `2` `m` is thrown at an angle `theta`. If their times of ascent are equal. Find the heights attained by them in ratio form.
- From a point at a height `h` above the horizontal ground, a particle `A` is projected with a velocity `v_0` in an upward direction making an angle `theta` with the horizontal. Another particle `B` is also projected with the same velocity `v_0` from the same point but in downward direction opposite to `A`. Show that the two particles will strike the ground at a distance: `(2u)/g * cos theta * sqrt((v_0)^2 sin^2 theta + 2gh)`

**Recommended Lessons**