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1. A particle is projected with initial speed 25 m s-1 at an angle of 30° above the horizontal. Find, to 3 significant figures, the maximum height the particle reaches above its starting position in metres.
2. A particle is projected from the ground with initial speed 10 m s-1 at an angle of 60° above the horizontal. How long, in seconds and correct to 3 significant figures, does it take for the particle to land?
3. A particle is projected horizontally with a velocity of 15 m s-1 from a point that is 20 m above ground. Find the horizontal distance, in metres and to 3 significant figures, the particle travels before landing.
4. A particle is projected horizontally with a speed of $u$ m s-1 from a point that is 100 m above ground. The particle lands at a point which is 75 m away horizontally. Find $u$ to 3 significant figures.
5. A particle is projected with initial velocity $4\mathbf{i} + 3\mathbf{j}$ m s-1. The particle lands on the ground after 5 seconds. Find the total displacement of the particle when it lands to the nearest metre.
6. A particle is projected from a point that is 30 m above the ground, with initial speed 12 m s-1 and at an angle of 45° above the horizontal. Find the distance the particle travels horizontally, in metres and correct to 3 significant figures, before landing on the ground.
7. A particle is projected from a point 24 m above the ground at an angle of elevation of $\theta$, where $\tan\theta = \dfrac{3}{4}$. The particle lands on the ground after 6 seconds. Find the displacement of the particle to the nearest metre.
8. A particle is projected from the ground with speed 40 m s-1 at an angle of elevation of $\theta$, where $\sin\theta = \dfrac{12}{13}$. Find the length of time, in seconds and to 3 significant figures, for which the particle is more than 10 m above the ground.
9. A particle is projected with initial velocity $3\mathbf{i} + 5\mathbf{j}$ m s-1 from a point that is 1 m above the ground. Find the angle the velocity of the particle makes with the horizontal as the ball lands.
10. A particle is projected with initial velocity $x\mathbf{i} + 3x\mathbf{j}$ m s-1 from the ground. It lands 30 m away from its starting positon. What is the maximum height, in metres, of the particle?
11. A particle is projected from the ground. The maximum height reached by the particle is 42 m,and the particle lands a horizontal distance of 196 m away. Find the initial speed, in m s-1 and correct to 3 significant figures, of the particle.
12. A particle is projected with an initial velocity $u$ m s-1 at an angle of elevation $\alpha$ from the ground. Show that the range of the particle is given by $$\dfrac{u^2\sin2\alpha}{g}$$ and hence find angle of elevation the particle should be projected in order for it to travel the furthest.
13. A boy throws a stone at an angle 30° above the horizontal from a point 1.5 m above the ground. The stone just clears the top of a 2.4 m tree which is 9 m away. Find the speed, in m s-1 and correct to 3 significant figures, of the stone as it passes over the tree.
14. A particle is projected from the origin with velocity $k\mathbf{i} + 3k\mathbf{j}$ m s-1, where $k$ is a positive constant. The position vector of the particle during flight is given by $x\mathbf{i} + y\mathbf{j}$ m. Show that $$y = 3x - \dfrac{gx^2}{2k^2}$$ and hence find, in terms of $k$, the maximum height of the particle above the origin.
15. A particle is projected with initial speed $u$ at an angle of elevation $\alpha$ above the horizontal. When it has moved a horizontal distance $x$, its height above the point of projection is $y$.
  1. Show that $y = x\tan\alpha - \dfrac{gx^2}{2u^2\cos^2\alpha}$
  2. A stone is projected from the top of a 15 m tall cliff with an initial speed 8 m s-1 at an angle of elevation of 40°. Find the horizontal distance, correct to 3 significant figures, the stone travels as it hits the sea.
16. A particle of mass 2 kg is projected along a rough horizontal surface with an initial velocity of 5 m s-1. The particle travels 1 m before leaving the surface. In the subsequent motion, the particle lands on the ground, which is 1.5 m below the surface. The total time the particle is in motion for is 2 seconds. Find, to 3 significant figures, the coefficient of friction between the particle and the surface.
17. Amy throws a stone downwards from the top of a 40 m tall building. The stone has an initial speed of 10 m s-1 at an angle of 30° below the horizontal.
At the same time, Ben throws a stone upwards with an initial speed of 12 m s-1 from the base of the building.
Given that the two stones collide in mid air, find the time, in seconds, between the stones being thrown and the collision.
18. A particle is projected from the top of a hill with speed $u$ m s-1 at an angle of elevation of 45°. The slope of the hill makes an angle of 45° with the horizontal and the particle lands at some point further down the hill. Show that the total displacement of the particle can be written in the form $k\dfrac{u^2}{g}$, where $k$ is a constant.