A projectile is launched at \(20\,\mathrm{m\,s^{-1}}\) and \(30^\circ\). Find \(v_{0x}\) and \(v_{0y}\).

A projectile is launched horizontally at \(8\,\mathrm{m\,s^{-1}}\) from height \(20\,\mathrm{m}\). Find time to hit the ground.

Why must horizontal and vertical projectile equations use the same \(t\)?

Using the previous setup, find the horizontal distance traveled.

A projectile is launched from level ground with \(v_0=30\,\mathrm{m\,s^{-1}}\) at \(45^\circ\). Find the range.

For a level-ground projectile, which launch angle gives maximum range when speed is fixed?

A projectile is launched at \(12\,\mathrm{m\,s^{-1}}\) vertically upward component. Find time to maximum height.

A projectile has \(v_{0y}=12\,\mathrm{m\,s^{-1}}\). Find maximum height above launch point.

A ball is kicked from ground level with \(v_{0y}=9.8\,\mathrm{m\,s^{-1}}\). Find time to top and total flight time.

A projectile is launched from \(y_0=10\,\mathrm{m}\) with \(v_{0y}=0\). Write the vertical position equation using upward positive.

A projectile has \(v_{0x}=15\,\mathrm{m\,s^{-1}}\) and \(v_{0y}=20\,\mathrm{m\,s^{-1}}\). Find its velocity after \(2\,\mathrm{s}\).

A projectile lands at the same height from which it was launched. If \(v_{0y}=18\,\mathrm{m\,s^{-1}}\), find total flight time.

A horizontal projectile falls for \(3\,\mathrm{s}\). How far did it fall vertically?

A projectile has \(v_{0y}=5\,\mathrm{m\,s^{-1}}\). Find \(v_y\) after \(1\,\mathrm{s}\).

A projectile is launched with \(v_0=24\,\mathrm{m\,s^{-1}}\) at \(40^\circ\). Find time and horizontal position when its velocity makes \(30^\circ\) below the horizontal.

A projectile is launched at \(25\,\mathrm{m\,s^{-1}}\) and \(37^\circ\). Approximate \(\sin37^\circ=0.60\), \(\cos37^\circ=0.80\). Find \(v_{0x},v_{0y}\), then find \(y\) when \(x=30\,\mathrm m\).

A projectile has \(v_x=10\,\mathrm{m\,s^{-1}}\) and \(v_y=-24\,\mathrm{m\,s^{-1}}\) just before landing. Find impact speed.

Using \(v_{0x}=20\,\mathrm{m\,s^{-1}}\) and \(v_{0y}=15\,\mathrm{m\,s^{-1}}\), find range on level ground and the speed at impact.

At what time is the velocity vector perpendicular to the initial velocity for a launch speed \(v_0\) at angle \(\theta\) \((0<\theta<90^\circ)\)?

A projectile has \(v_{0x}=18\,\mathrm{m\,s^{-1}}\), \(v_{0y}=14\,\mathrm{m\,s^{-1}}\). Find the flight time and horizontal range if it lands \(6\,\mathrm m\) below launch level.

A target is at \((x,y)=(40\,\mathrm m,12\,\mathrm m)\). A projectile is launched from the origin with fixed speed \(v_0=30\,\mathrm{m\,s^{-1}}\). Determine all possible launch angles and state whether the hit is feasible.

A projectile must clear a wall of height \(15\,\mathrm m\) at horizontal distance \(25\,\mathrm m\), then land on level ground at \(60\,\mathrm m\). Find the minimum launch speed and corresponding angle.