Projection from elevated point - angle below horizontal or horizontal

6 A particle \(P\) is projected with speed \(26 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at an angle of \(30 ^ { \circ }\) below the horizontal, from a point \(O\) which is 80 m above horizontal ground.

1. Calculate the distance from \(O\) of the particle 2.3 s after projection.
2. Find the horizontal distance travelled by \(P\) before it reaches the ground.
3. Calculate the speed and direction of motion of \(P\) immediately before it reaches the ground.

7 \includegraphics[max width=\textwidth, alt={}, center]{e85c2bf4-21a8-4d9a-93c5-d5679b2a8233-4_440_657_906_744} A ball is projected with an initial speed of \(17 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at an angle of \(25 ^ { \circ }\) below the horizontal from a point on the top of a vertical wall. The point of projection is 8 m above horizontal ground. The ball hits a vertical fence which is at a horizontal distance of 9 m from the wall (see diagram).

1. Calculate the height above the ground of the point where the ball hits the fence.
2. Calculate the direction of motion of the ball immediately before it hits the fence.
3. It is given that \(30 \%\) of the kinetic energy of the ball is lost when it hits the fence. Calculate the speed of the ball immediately after it hits the fence.

A particle is projected at an angle of \(θ°\) below the horizontal from a point at the top of a vertical cliff \(26 \text{ m}\) high. The particle strikes horizontal ground at a distance \(8 \text{ m}\) from the foot of the cliff \(2 \text{ s}\) after the instant of projection. Find

1. the speed of projection of the particle and the value of \(θ\), [6]
2. the direction of motion of the particle immediately before it strikes the ground. [3]

A particle is projected at an angle of \(θ°\) below the horizontal from a point at the top of a vertical cliff \(26\) m high. The particle strikes horizontal ground at a distance \(8\) m from the foot of the cliff \(2\) s after the instant of projection. Find

1. the speed of projection of the particle and the value of \(θ\), [6]
2. the direction of motion of the particle immediately before it strikes the ground. [3]

A particle \(P\) is projected with speed \(20 \text{ m s}^{-1}\) at an angle of \(60°\) below the horizontal, from a point \(O\) which is \(30 \text{ m}\) above horizontal ground.

1. Calculate the time taken by \(P\) to reach the ground. [3]
2. Calculate the speed and direction of motion of \(P\) immediately before it reaches the ground. [4]